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.
Possibly. I asked (and no one’s answered yet, so I still don’t know) if it’s still a Mercator projection if you vertically bisect a map of the Earth.
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.