Taking a second look at that, though - is that really a continuous projection? Or is that storing different parts as different chunks (and maybe projected differently) put together into the one image?

Huh, neat!

It’s still a Mercator projection if you take any part of a map projected thusly. (And there’s the “modified universal transverse Mercator” that, I think, is that with some grid offset.)

But, see my edit, this image isn’t doing that. It’s stretching a “picture of half a face superimposed on a larger half globe,” not the half-face as if the head were the globe.

This has got to be wrong. A human head, projected like a world map, would show both eyes and both ears, except in the case of showing only one half (like when you only show/photograph the Americas).

This appears to take a picture of the side of the head (i.e. that particular projection, showing less than half of the full globe), then distort it as if it were already a different projection.

Edit: worse than that. The globe onto which the half-head-image is superimposed in the top right is larger than the head. Like if you took a photo of the Americas half of the world from space, pasted that onto a larger beach ball, then stretched the result to demonstrate the projections.