IANAL either, but I suppose the situation here is similar as with "abandonware": as long as the original publisher/copyright holder doesn't protest, old software is made available on various download sites. Of course, with a project like this, if the copyright holder would intervene, a lot more work would go down the drain, and claiming your own copyright without explicitly mentioning the original copyright is definitely not helping...

> but I suppose the situation here is similar as with "abandonware"

I don't know if this would hold up. Prince of Persia IP is far from dead or abandoned. I know it's not exhaustive, but a quick search on IMDB [0] shows a movie in 2010, and a video game as recently as 2008. Just because this particular game is old, doesn't mean the IP/Trademark is dead. Personally, I'd be wary of a legal battle, even though I think the project is pretty interesting.

[0] https://www.imdb.com/find?q=prince+of+persia&ref_=nv_sr_sm

Again, IANAL, but that's not really relevant. The old Super Mario games for Game Boy and SNES can be downloaded from various abandonware sites, while the Mario franchise is still ongoing. As long as Nintendo is Ok with that, that's not a problem. The original Prince of Persia is also available as "abandonware" and can even be played in the browser (https://www.retrogames.cz/play_102-DOS.php?language=EN)

Even if Nintendo is OK with that (are they really?), that does not mean that someone else can grab one of those copies and claim copyright on it! That's what the author of the reverse-engineered Prince of Persia seems to be doing.