I really enjoy having non-Euclidean dungeons in my campaigns. My players also enjoy them. But the whole idea of warped geometry tends to rely on magic. How, if at all, could I explain a non-Euclidean dungeon in a different setting?
I'd need to be able to drop hints to my players about the nature of the dungeon beforehand without making it explicit that there will be non-Euclidean geometry.
Examples of the sorts of things I like to include are doors that lead to the ceiling of a room while going in a completely straight line, a hole in the floor that comes out of the ceiling, leading to a never-ending fall, and having five rooms in a pentagon, where each corner is a right angle.
The sorts of settings I mean are as varied as Science Fiction and Modern to Pokemon RPG, so answers that don't rely on setting or genre-specific factors would be better, but anything non-magic is good.
Best Answer
The Difference between Magic and Non-Magic is Usually Fluff
In plenty of settings and games, magic is objective, such as in D&D and Ars Magica. You can easily refluff "magic" to be clear "science" instead; after all, it's only the way reality works.
Use Warped Dimensional Spaces/Basement Universes as an Explanation
The hints that a dungeon works in a non-euclidean fashion can be explained as a warp space where the laws of reality apply differently, or a wormhole that leads to a basement universe in which physical laws are different. If you have the will for it, and your players enjoy this sort of thing, go ahead and look over the axioms of Euclidean geometry and change or remove them as you see fit: real life non-euclidean geometry doesn't have the Parallel Postulate, for example.
Distortion World from Pokemon Platinum is a good in universe example
The physics of distortion world are wonky, allowing traversal up and down certain areas through gravity, walking upside-down on certain platforms, and certain objects appearing as you walk near to them. This isn't "magic" flavorfully, as it's where Giratina resides as a kind of opposite number to Dialgia and Palkia, so if you're looking for Pokemon specific fluff to your non-euclidean maze, this is it. If you're looking for an oddly meta take on things, check out Glitch City, from a glitch in the Generation 1 games that leads to a city that is inescapable without flight.
Other suggestions for refluffing a non-euclidean dungeon could be
Unfortunately, I can only provide so many examples of ways to refluff, but I'm certain you can come up with many on your own. In essence, physical laws work differently for reasons that are non-magical in nature, and the rest is up to you. I can expand this answer more if you're looking for examples of implementation as well. Good luck!