The 2D part is well explained, however, I am interested in how they made it 3D. They have voxels, but the actual rendering is a bit unclear.

I guess they simply didn't do much work on that part, using some bruteforce-ish raymarching technique, which their fast evaluation and nicely bound objects allows. They mention further work though, like sparse voxel octrees, improving culling, etc... So I guess that will be for a "future episode".