[earenndil]

Hyperrogue[1] takes place in hyperbolic space. Definitely a good way to gain an intuition for it. It offers several different projections, so you can try them out. It's also open source[2].

1: https://roguetemple.com/z/hyper/

2: https://github.com/zenorogue/hyperrogue

[abnry]

Another game to check out in this vein is hypernom, developed by henry segerman, vi hart, and some other people that I don't remember: http://hypernom.com/

[eru]

In a less principled way, there's also 'Antichamber' and 'Tea for God'.

Both use Escher-like spaces that are locally Euclidean but don't connect in proper ways. Eg if you go 360 degrees around a column, you might arrive at a different place in the level from where you started.

In Antichamber it's an interesting gimmick. In 'Tea For God' the mechanic is actually useful, because it's a way to fold a big level into the small boundaries of the VR space you defined on the Oculus Quest in your living room.