Being on a hyperbolic surface instead of strictly flat is certainly non-Euclidean, and this is pretty cool.
Another non-Euclidean approach is that taken by Vicious Orcs: each individual room is Euclidean, and the player can't tell that he's moved from one room to another, but the connections between rooms are arranged such that the overall map doesn't fit in a plane or even a 3 dimensional space. I got very lost and did not finish the game.
That's not all! I know of two other non-Euclidean seven-day roguelikes (7DRLs) Jeff Lait has made. And a very large number of 7DRLs in general. I definitely recommend looking through his games, Jeff Lait has used many wonderful concepts.
For other non-Euclidean space example (although not hyperbolic) there is Antichamber (http://www.antichamber-game.com/). But in general, not only space whole reality was distorted/dream-like in this game.
Another non-Euclidean approach is that taken by Vicious Orcs: each individual room is Euclidean, and the player can't tell that he's moved from one room to another, but the connections between rooms are arranged such that the overall map doesn't fit in a plane or even a 3 dimensional space. I got very lost and did not finish the game.
http://www.zincland.com/7drl/orcs/