Based on the examples on the page, here's how I think it actually works: The projection center is not a single point in space but rather varies along the optical axis depending on the position of the 3D vertex as seen from the camera. More specifically: For each vertex a preliminary linear projection is computed to get an XY position, then the projection is recomputed using the preliminary XY position, where things near the center are re-projected using a projection center that is moved forward along the opt. axis and things near the borders/corners of the image have it moved backward. On top of this then probably a standard fish-eye.
That said, I'm not sure this whole projection trickery is really worth it, given that it comes with its own issues (your scene will appear to warp when you turn the camera) and given that you can probably get 90% of the value with one of the more standard fish-eye models.