The perspective is still from a two dimensional point of view because that's how we perceive visual information. In two dimensions, it's impossible for us to VISUALLY perceive something in ACTUAL three dimensions or four purely because we have to be able to look at all of the angles of interest to do so. The visual in that GIF is merely a guide to help us out with the admittedly abstract idea of what a different dimensional "space" would look like.
Just to make you understand, a one dimensional individual would only be able to visually perceive objects in 0 dimensions, a two-d individual in one, a three-d in two, a four-d in three and so forth.
