Play a Portal-like game in a room in which passages among through walls connect to other walls.
Or on a surface of a hemicube. Or other abstract polyhedra or polychora (11-cell, 57-cell) though I am less sure how the latter would work, as the hemi-polyhedral cells don't seem to be manifolds.
Play in 2D or 3D hyperbolic space, maybe flight simulator.
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