My head is spinning from reading this thread.
The issue here is what is conventionally accepted as an "open world" game. I don't recall this being a term that was tossed around in 1994, back when Alien vs. Predator was released.
"Open world" seemed to take shape with the release of Grand Theft Auto III in 2001. The game was a marvel at the time, with a huge environment that was fully 3D rendered. There were distinct places that you could visit, leave, and revisit later. There were all sorts of non-player characters roaming around, that you could interact with in various ways. There was always somewhere to go to find a mission to do...or you could just roam around and do nothing in particular at all.
After GTA3, you had other games that expanded on the concept, like Assassin's Creed, Red Dead Redemption, Horizon Zero Dawn, and more. They all embraced the freeform style of gameplay, where you could advance the main story, tackle some side mission, or just go exploring and sightseeing.
Would I consider Alien vs. Predator an open world game? Well, relatively speaking, it is more "open" than most first-person shooters of the day, like Wolfenstein 3D and Doom (both of which were on the same system). Those games were focused on completing distinct levels in sequence, while AvP's levels are all interconnected into one large playing area. You can freely go back to any area of the game environment that you previously visited. So, it does satisfy one aspect of "open world" games.
The overall game does not fully satisfy the conventional definition of "open world", though. Although you have three characters with different play styles, each one of them still has a singular goal throughout the game. There are no side missions, and all of the NPCs are distinct enemies with rigid behavior patterns. It's actually structured more like a Metroidvania (another modern gaming term). It has about the same amount of freedom as a game like Castlevania: Symphony of the Night, which is not necessarily a bad thing. I think both the third and fourth poll options would apply here.
Come to think of it, is Raiders of the Lost Ark (1982 game for the Atari 2600) "open world"? Probably not, but it was rather advanced for its time. It even had Metroidvania elements such as inventory management, and areas that can only be accessed after certain items have been obtained and properly utilized.