I might be missing something but you sound genuinely confused to me. The perspective in your post is linear perspective. It's the one used in CSS and it doesn't curve straight lines/planes. It's not the perspective of fish-eye images (curvilinear perspective).
I was at least a little confused because yea fish eye isn’t possible with a 4x4 perspective transform matrix. I’m investigating an issue with the projection thanks to some help from commenters and there will be a correction in the article, as well as an animation which should help confirm the projection code.