Quoting from the site:
A peculiar sort of remapping for spherical panoramas that makes everything look like an illustration out of The Little Prince.
Basically, to make these, you have to make an equirectangular first. Your best resources for learning how are panomundo and panoguide. It’s not easy and is rarely cheap.
From there, you remap the equirectangular in one of two ways. You can resize it to a square and convert from Cartesian to polar coordinates (you can even get away with non-360 panos) or you can do a Stereographic remapping using the open-source Hugin, the GIMP Mathmap plugin, or the Photoshop shareware plugin, Flexify, then crop.
Good grief – and I think that Photoshop 101 is hard!