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Where people live just meant that choosing to distort the equator. This does not seem like a useful map to use if you are interested in Africa or South Asia! It's a tradeoff for all projections.

However, I don't want to go too hard on these guys. Reading the arXiv paper, I think it's clear that they wanted to make a cool set of disks for the Solar System. They actually look really cool for Jupiter and Saturn with their equatorial cloud bands and polar vortices! And centering on the poles gives a nice symmetry with the Earth and Mars with the ice caps.

They also show the version of Earth with the projection centered on the Western and Eastern hemispheres and the distortions are a lot more obvious (e.g., Alaska, Canada, and Australia are pretty bad). I can see why they like the North/South pole version.