> This is done using WebGL, an API for drawing 3D graphics in a browser. You might think it's only designed to draw ordinary, Euclidean things, but it turns out it's perfectly suited to rendering this world as well. WebGL (and OpenGL) works with four-dimensional coordinates (x,y,z,w). Normally, you'll be advised to just set that w coordinate to 1 all the time. If you do that, the x, y and z coordinates will behave like ordinary 3-D geometry. I just ignored that rule and used the coordinates to represent points on the 3-sphere instead. It all works out. (You have to be a bit careful if you want to put textures on things without seeing seams between the triangles, but it can be done. The key is to make sure every flat surface is still a flat surface in 4-D.)
Are the 4D coordinates treated as ratios, so that (w,x,y,z) = (tw, tx, ty, tz)? Because then that would express RP^3 instead of S^3, i.e. projective 3-space, instead of the 3-sphere. Equivalently, this produces a model of 3D elliptic geometry, instead of 3D spherical geometry. My doubts are because 3D computer graphics is known to use homogeneous coordinates, which results in a model of projective 3-space or elliptic 3-space.
S^3 can be coordinatised using elements of R^4 of unit length, which might have been done here.