By that logic, the game Portal is non-Euclidean. Which might be true in a certain interpretation. But nobody looks at portal and thinks itβs anything but a normal 3D world with portals.
Here the geometry is very unusual. But using the existence of portals to define that seems insincere.
It is non-Euclidean. 4 out of 5, if not 5 out of 5, of the postulates that define Euclidean space fail. It can't fail any harder.
This isn't a matter of emotion or feeling like "oh, gee, I don't want to, like, demote the space or make it feel bad for calling it 'non-Euclidean'." This is math. The postulates won't work. The proofs won't hold. Even a single portal in the space make it non-Euclidean. It doesn't fall down a little bit. It doesn't "mostly hold, you know, except for a few exceptions". It breaks the axioms from top to bottom.
Here the geometry is very unusual. But using the existence of portals to define that seems insincere.