They are absolutely within their rights to approach the developers of Ryujinx and threaten to sue them. Based on how things have worked so far they'd lose, and I agreee with you that the inequality in that interaction is terrible and should be addressed.
On the Yuzu scenario it's more relevant, because of the specific proprietary elements found in the emulator.
And then there's Nintendo targeting emulation-based handhelds and streamers for featuring emulated footage of their first party games on Youtube videos, which falls directly under the mess that is copyright enforcement under Youtube and other social platforms.
In all of those cases, a clearer, more rules-based organization of IP that explicitly covers these scenarios would have helped people defend against Nintendo's overreach, or at least have a clearer picture of what they can do about it. We can't go on forever relying on custom, subjective judicial interpretation and non-enforcement. We're way overdue on a rules-based agreement of what can and can't be done with media online.
The worst part is... we kinda know. There is a custom-based baseline for it we've slowly acquired over time. It's just not properly codified, it exists in EULAs and unspoken, unenforceable practices. It's an amazing gap in what is a ridiculously massive cultural and economic segment. It's crazy that we're running on "do you feel lucky?" when it comes to deciding if a corporation claiming you can't do a thing on the Internet that involves media. We need to know what we're allowed to do so we can say "no" when predatory corporations like Nintendo show up to enforce rights they don't have or shouldn't have.