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.
I think we both love Math. But I respectfully disagree. These are games. In a game like Portal, standard intuition about geometry mostly applies, as long as there isn’t a portal in the portion of space you’re considering. The boundaries between reality and magic are what make it interesting. And the fact that it’s mostly normal but sometimes not is exactly what makes it interesting. Because for the player, it doesn’t matter if the proofs are invalid, their intuition mostly holds.
In HyperRogue, normal Earth intuition is mostly inapplicable because of the hyperbolic geometry. The fact that it has portals and therefore proofs fail shouldn’t IMHO be the defining features of the world. Unless you think the key audience of the game is topologists or something, but if you care about non-mathematicians getting into the game, I’d say focus on intuition not axioms.
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.