Not sure what you mean -- with portals you still get locally Euclidean space -- "locally" usually means "in a sufficiently small neighborhood", and even if you are on a portal, you cannot tell from a small neighborhood, all the points in that small neighborhood will have only one straight line connecting them through the neighborhood, and all the small triangles will add to 180 degrees.
It does not make much sense to say that a game is non-Euclidean just because it violates some Euclid's axioms -- then you could say that any game taking place in a bounded world is non-Euclidean because Euclid's axioms say that lines can be extended infinitely, or any grid-based game, or any game with no space at all, or any 3D game because Euclid's axioms are for planar geometry, etc.
The interesting thing is replacing Euclid's parallel axiom while all the remaining ones remain unchanged. (Likewise when you say "irrational number" you still mean a real number, not anything that is a number and not rational.) Euclid thought that this was impossible (and that the parallel axiom actually follows from the other ones), so did people for 2000 years, and when it was discovered this was possible, this was called "non-Euclidean geometry". Later extended to other things similar in style, but portals do something totally different.