Actually, of course, the AvP movie started out (before the FPS games, by the way - but not before the console games which started just after the comics) as an attempt to adapt the generally excellent Aliens vs Predator comic. Along the way, as with all scripts in Hollywood, it went through major changes (the earliest leaked script I've seen had already moved the action to a jungle setting, rather than the desert/prairie of the comic), ending up in the significantly dumbed-down, and totally different AvP film that we actually got. This entire process took something like a decade+ (the comic was released in the early 90s, and the film seems to have entered script writing somewhere in the mid 90s...).
Coming back to the original discussion - I fully support the idea of a randomly occurring Predator (guaranteed in any given game, but randomly located), but it does seem a little unfair to let people use its equipment. (That said, there is at least movie-canon for the throwing disk being human-useable...)