[brianshaler]

I made an interactive WebGL implementation of this without realizing it was a thing: https://brian.sh/around/index.html

I don't really agree with the claims in the articles linked in OP, and don't find it to be a generally useful projection, even for the tool I made using it. It was novel as a representation that included daylight context (instead of just "what time is it there?" it helped express "is it getting dark there?") that preserved area better than a globe and was more intuitive than a day/night waveform on a rectilinear projection. But ultimately, if you're showing anything that has to do with populations (cities, people) pretty much any projection will waste large amounts of space on oceans and unpopulated land regions. That is to say, before choosing a favorite map projection, I think it's probably better to not to use a map projection at all unless you're going for a hike or setting sail.

Somebody beat me to the obligatory xkcd, but this West Wing bit is my go-to for map projection discussions: https://youtu.be/vVX-PrBRtTY

I like framing map projections by what they prioritize or sacrifice—fidelity in axis, position, size—and what projection is "best" depends entirely on which characteristics are more important. I disagree with OP's claim about this projection being "the most accurate flat map of the Earth yet" though haven't put a ton of thought into the physical, back-to-back definition of "flat" vs on-screen.