It almost looks like they mixed training and testing data in some of the examples. The bottom-left sample in the normals-to-faces is extremely suspicions.
I was looking at this as well, but I'm willing to suspend my disbelief because the normal vaguely looks like it has a good deal of information (in a basic fidelity sense).
seems astonishing that the normal information includes enough detail to tell you which direction the eyes are pointing, though?