how was rebellion able to release this game, considering they don't own the IP or the publishing rights, they did AVP 2010 by Sega/20th Century so did they re-license the game?

By Spinorial: "As far as I can tell, Rebellion has retained/acquired all rights for the digital distribution of the game. You're worried about SEGA, but they only acquired the licence sometime after 2005, and that has no bearing on the previous entries in the franchise. They may, at some point, buy these rights from Rebellion and the other past rights-holders, but right now there's no indication that they have anything to say about these."

https://www.gog.com/forum/aliens_versus_predator_classic_2000/who_owns_the_rights_to_the_title