Hmm, sounds like a lot of sales talk around what seems to be a "nice fisheye effect".
The first gif of that room in the article shows exactly the problem: rasterizing works by transforming a bunch of triangles from world space to view space.
This works with rectilinear projection because each triangle can be transformed into a different shaped triangle, based on the perspective of the camera. You can't transform a triangle into a "bendy" triangle. And the screenshots show "bendy" lines.
So, if you want a "fisheye" effect in rasterization, you first need to render a rectilinear image, and then distort it, leaving you with a blurry center due to a lack of resolution.
Regarding the "volumetric" bit, I think it just means that the camera is moved forward just a little bit.