So far as anyone is aware that song is literally the only issue.
Sega managed to muddy the waters a lot because one of their people initially said that the rights to the game had expired (with the inference that Obsidian owned it now), but it was later clarified to music rights and that is the only licensed music in the game. IIRC it isn't even a song that would be heard in many playthroughs, and you only get it/ the stereo that plays it by handling the Moscow missions a particular way.
I presume a fix would literally involve sticking in a replacement generic muzak wav/ ogg or whatever as a replacement, but Sega seems to want to pretend AP never happened so cannot be bothered. Source
I don't know how technically challenging that could be but it sounds like an easy fix, if indeed that is the only legal issue. It plays during a boss fight with an "80s obsessed Russian mafioso" apparently. Surely there's a generic '80s sounding song replacement. (Or GOG just removes it and has no music play, not ideal but whatever could get the game back up.)
In any case, the game has over 2,000 combined votes on the wishlist - https://www.gog.com/wishlist/games#search=alpha%20p&order=votes_total
so I believe GOG would love to have it here (especially if they get it for a period of exclusivity before it would return to Steam).