It can if the engine makes the game run poorly or not at all (I wouldn’t buy it) or if the engine is exceptionally well regarded and runs great it might make me a bit more inclined to buy the game.

If it’s an engine famous for being janky, it might also make me delay buying the game until devs or modders fix it.

Also, if the engine is known for being mod friendly, that would probably make me more inclined to consider buying the game.