I’ve on my way to work but I’m commenting so I can come back and give you a list and see what everyone else suggests.

There’s a game called Journey which is… mystically beautiful? It’s mystical because it’s basically just a walking sim with a few puzzles to solve in between, but yet it really draws out the emotions. I’ve played many games like this but nothing trumps Journey yet.

It’s mostly single player but if you play it online, once in a while you’ll come across a fellow traveler from another instance whom you can share the journey with for a while, or not.

You’ve come to the right place, I also fancy artsy games and unique experiences.

• Return of the Obra Dinn is a great mystery game about figuring out who died and why. You use your watch to go back in time and explore the moment of death of everyone, trying to piece together what happened.

• Viewfinder is a new puzzle game where you take pictures of your surrounding and place them in front of you, turning them back into 3D-space

• Antichamber might be my favorite abstract puzzle game ever. It’s hard to explain and can be a little obtuse (you get lost easily), but basically you explore a lot of world-shifting environments and try to figure out what is needed. Eventually you get a gun that manipulates cubes and stuff. Really, just play it.

• Manifold Garden is a close second after Antichamber. You explore infinitely repeating worlds and shift gravity to solve puzzles. It’s not a hard game and you can finish it in a few hours, but it’s a great experience.

• Journey is probably a game you’ve come across before. I loved this game to death when I first played it on PS3, I’d recommend giving it a shot. It’s also quite short, only about 3 hours long.

• Hypnospace Outlaw is a game where you play on a fake late 90’s operating system acting as a web moderator. I can’t understate how cool this game is, and the seemingly innocent story gets more interesting as you play along.

There’s probably more out there, but these are on the top of my head.

Don’t know how well known it is, but Who’s Lila is a point and click adventure game when you progress by controlling the character’s facial expressions

The Unfinished Swam came instantly to my mind.

Some others that might intrest you but I’m not sure really qualify with the description: Roto force - Quirky take on a bullet hell game Yukos Island express - Metroidvania pinball The Witness - Well known puzzle game that has you looking for 2D shapes in 3D areas, and other things Quantum Break - Mixing TV between chapters, didn’t live up to it’s potential in my opinion

I dont know if it still can be found, but Achron is a Time travel strategy game. Think command and conquer where you can send orders and troops in the past. One the change is done, the effects will travel in the time line as a wave. Fixing the paradoxes Letting you send troops back 5 minutes giving time clones for the attack.

youtu.be/rGmMenc1jCY

SUPERHOT - a shooter in which time only moves when you move. It kind of plays like a puzzle game and is quite fun

Superliminal is a fun puzzle game that plays with perspective to find out-of-the-box solutions.

Virtamate fits your description

Toribash is a unique take on fighting games, where you control the character in freeze-frames by adjusting actions on the character’s joints (relax, hold, flex, extend), then executing those actions. You can make singleplayer sequences or fight other players one on one - you get X amount of seconds per move simultaneously with your opponent, then the movement is resolved and you have another action round.

Omega Strikers - I’m not sure if this fits the bill entirely, but I think it is relatively unique in what it does and I have been playing the heck out of it since release, so I’ll plug it. It is a mesh of MOBA and table hockey, the game plays in 3v3 - 2 forwards and a goalie each team. Controls relatively standart for MOBA, the goal is to get the core (puck) into the enemy goal. You can also knock opponents off the sides or damage them making it easier to knock them off.

A fairly unique game that I've played and have never experienced anything like it since, is Doki Doki Literature Club. It's very easily spoiled, but one must be forewarned it is psychological horror and it's warning at the beginning of the game is on point. It's radically different than anything else here, but there's also nothing like it that I can think of to compare it to. Sure, it's basic gameplay is "visual novel" but it goes way beyond that. Again, it's absolutely a psychological horror and it does touch on extremely sensitive topics. So avoid if that sounds problematic, but as a standalone work, it honestly creates a category all its own and I'll likely never play a game that recreates anything close to it.

And totally different but a lot closer to other suggestions is the game Bastion. Very interesting time-manipulation puzzle solving with a intriguing plot story that doesn't steal the focus but is still good enough to add value to the game.

Miegakure is probably something you’d be interested in. miegakure.com

Give Up the Ghost - https://gate.itch.io/ghost

I've always wanted to back and beat this puzzle game, because it's quietly excellent.
There's some proper rot13 hints in the comments by the creator.

If you want a somewhat curated list of wild games I can recommend Warp Door - https://warpdoor.com/

So I would also recommend Antichamber, Manifold Garden, and Unfinished Swan. I would also add the following:

What Remains of Edith Finch - while technically a walking simulator it really does provoke a child like sense of exploration while providing a very adult storyline.

Thomas was Alone - this is a platformer at heart but the minimalist design, innovative mechanics, and great storytelling make this game a must play.

The Spectrum Retreat - this is technically a Portal clone but the puzzle mechanic is based on color and manipulation of environment. The story is bleak but compelling. And as the story progresses your view of the hotel changes adding to the tension.

The Bridge - not going to lie this puzzle game gets brutal but the mechanics are like nothing I’ve ever played before or since. You navigate through Escher-like environments. If you can get it cheap and don’t mind using a help guide I’d say go for it.

Honorable mention/good time wasters:

Hexalogic - number puzzler and great zen experience. I’ve not found another game like it and I wanted more when I finished it.

Inbento - a cute puzzle slider game where the board is a bento box. The game introduces more mechanics as it progresses and it gets hard.

Inscryption, there’s a reason it’s such a highly rated game on steam.

store.steampowered.com/app/1092790/Inscryption/

Inscryption is an inky black card-based odyssey that blends the deckbuilding roguelike, escape-room style puzzles, and psychological horror into a blood-laced smoothie. Darker still are the secrets inscrybed upon the cards…

might not be what you are looking for but i strongly recommend project zomboid for the best unique costumizable survival game

Planescape: Torment
The story of an amnesiac immortal piecing things back together.
The immortality isn’t invincibility, you still die, but wake up after a while.
Die enough times and you lose all memories, maybe with a different personality altogether, that’s where the game starts: a cold slab in the morgue and the start of this new incarnation you now control.
It’s not only a respawn mechanic though, the mechanic is used in a few puzzles and social encounters, it’s also integral to the storyline.

If you want weird go Eastern European

Cryostasis: Sleep of Reason - stuck on a nuclear ice breaker where you have to play back frozen members of the ships cause of death and save them. In addition to this the core health mechanic is the most unique I have found in a game where health is decided by how warm you are so you can recover off steam pipes and can as lose health in colder regions of the ship

The void - I don’t know too much about it since I never managed to complete it but this is really odd. It’s like Okami but I’m sort of this hellish weird world. You have to draw shapes to do things like attack enemies. Plus again another health system where you lose health as you stay on the menu screen very weird.

There are a lot more and all tend to be fairly bleak but cyrostasis I 100% recommend the story is just as good as it plays out through those death scenes

Since nobody mentioned it before, Stanley parable.

If I had to describe it with one sentence: you’re not playing the game, it plays you. I played a lot of games but this one stuck in my head. It awards for thinking outside the box.

Any other title like antichamber were already mentioned ^^

TUNIC youtu.be/Q5XpgTO7YN0

On the surface it’s a Link To The Past inspired Zelda clone, with hints of Dark Souls, cutesy graphics, and a KILLER soundtrack. And while that might sound appealing, it’s really just the surface. This game does something so unique that I can’t imagine how it could be done again in any other game.

Undertale? I came at it being basically familiar with RPGs and having only a faint idea of what it was like. It was awesome. It has a few things that get "rosebudded" a bit these days, being an old game with a bunch of meme potential. It's an indie, very Japanese-inspired RPG with "bullet hell" fighting mechanics and an astonishing soundtrack. I basically can't praise it enough, BUT if you're going to play it and have managed to not get it spoiled so far, do yourself a favor and don't read up on it first.

Factorio? I fell in love with it practically because of the nice, flashy power graphs. It's a factory sim with "tower defense" aspects but you can play peaceful mode if you (like me) are not into that or don't like its combat mechanics.

TIS-100, Shenzhen IO, SpaceChem, Opus Magnum or Zachtronic games in general, if the last one was somehow not geeky enough. A lot of the zachtronic-style games have more or less the same general idea and they also focus on some nostalgia/zeitgeist type things. TIS-100 and Shenzhen IO are coding games on an imaginary computer, you basically write a minimal form of "assembly". SpaceChem and Opus Magnum have the same basic problem solving thing but are less overtly "code-y".

This ended up a bit longer than I intended, whoops. Most of your examples are more conceptually unique than most of these, but I figured it couldn’t hurt to mention them since they all do something ‘different’ you might find interesting. I’ve really enjoyed all these games myself.

• Perspective - Absolutely mind-blowing, this is the one that I think fits your question best. There’s both walking around in a 3d environment and 2d platforming, but the platforming is based on your perspective. It’s hard to describe, but it’s free (college project), so go check it out!
• Cortex Command - I wouldn’t exactly call it experimental, but it’s certainly unique. The selling point is the fully destructible particle-based 2d environment. It may be 20 year old abandonware, but there’s a reason it still has an active fanbase working to improve it (check out the Cortex Command Community Project).
• Antichamber - Reality-bending first person puzzler. It can be frustrating at times but it has some seriously mind-boggling challenges.
• Little Inferno - You burn things. It’s amazing.
• Reassembly - Hard to describe, kinda like 2d space legos with some strategy elements? You build spaceship things and slowly amass your army, gathering resources and commanding your fleet. It’s a bit sandboxy for my taste but I’ve never played another game with this unique mix of strategy and building. It’s a lot of fun seeing the ships you create flying around independently, gathering resources, fighting enemies and even making more ships themselves.
• Melody’s Escape, Beat Hazard (1/2/3), Symphony - I’m a big fan of games that use music for generating levels, and these are my favorites. It’s a small ‘genre’ but it’s fascinating to me to see how different developers approach it. Melody’s Escape is a rhythm game which is pretty unique among this ‘genre’, Beat Hazard has spectacular visuals and adds in progression (with varying degrees of success), and Symphony is pretty similar to Beat Hazard in basic conception but executes things differently at every level.
• Sanctum 2 - Combination tower defense + FPS. The unique thing about this is less the idea and more how well it’s executed. A ton of fun with friends.
• Yoku’s Island Express - Pinball metroidvania-lite. What can I say, they make it work.
• The Beginner’s Guide - A linear story / adventure game sort of thing. The setup is essentially about exploring different short games made by someone who committed suicide. It’s slow and sad, but has a unique concept that it executes well. It has a couple of twists that really make the game.
• Shelter 1 & 2, Meadow - Shelter 1 is a linear adventure game where you play as a badger mother caring for her pups. Shelter 2 is a nonlinear survival game where you play as a lynx mother caring for her… kits? Then Meadow is a sandbox social MMO in the same universe, with little goal aside from just interacting with other players; but there’s no text chat, only a limited set of emotes and some actions you can do. This is a great little family of games, each being an entirely distinct and unforgettable experience.
• The Messenger - Starts out as a linear 8-bit-styled action platformer that (spoilers) turns into a 16-bit-styled metroidvania. Conceptually that’s all that really makes it unique but it’s done well, lots of fun.

Recently I’ve been exploring flash games again. I played them a lot as a kid, but in revisiting them I’m blown away at how unique and interesting so many of them are. Here are a few of the more unique ones you might enjoy, you’ll have to use something like Flashpoint to play them:

• This Is The Only Level - There’s one level, but the mechanics change each time you complete it. Super fun.
• Demons Took My Daughter - A combination 2d platformer and tower defense (complete with mazing). It’s worth checking out all of the developer Nerdook’s games, he has a habit of mixing genres in completely new ways.
• This is not a minimalist game - A short adventure game, nothing groundbreaking but has some interesting ideas.
• The Day - This is a weird one, kind of hard to describe without spoiling it but it’s like <20 minutes to beat, mostly just a walking simulator sort of thing. The game’s dev, Gregory Weir, has a lot of experimental games, if you like this one you’ll probably like more.
• Sugar, Sugar - A really unique puzzle game, its basic idea is simple but it makes the most of it. Another dev to check out more from.

Outer Wilds.

but a game where the plot twist is discovering a hidden game mechanic, you could’ve done all the time

Turn this up to 11.