I think the point is not to talk about how it's implemented, but to point out that it's a more complex change, one that cannot be achieved by first performing a traditional render and then transforming the resulting 2d image. You actually need to project differently.
And how should that be more natural, as they claim?
A human eye is just a lens. With very well studied geometry.
The brain can do amazing feats, e.g. make bend/warped parts of images it sees straight again. A friend of mine who's 20 year old LASIK is coming apart, unfortunately, experienced it first hand recently.
But it can't see behind objects.
So if the occlusion changes as, they claim, there are two possibilities:
1. The camera was moved.
2. The scene geometry was distorted. That is possible in a computer but not in reality.
I.e. the result can never be more natural than what you can already model with a 2D fisheye projection based on human eye geometry.
