I've got to reconsider given adrusi's comment, I think he's actually right. The parallel postulate is what makes the sum of angles of any triangle to be 180º.
While it can be useful (or not) on the applications described, this is not non-euclidean. It is pure euclidean, but defined in steps.
I agree that is visually exciting and all that jazz, but this has nothing to do with Non-Euclidean Geometry... My surprise is that I though this video will give some 3D intuition on this topic, but nay.