I envision a Predator game acting similarly to Resident Evil or really the remakes.
My pitch is an open-world title set in the first person where the player chooses one of three campaigns. A gang member or average citizen caught up in a gang war, a police officer, and either an OWLF or Stargazer agent depending on when the game is set. The campaigns in effect act as difficulty modes because of how the Predator chooses targets. The Predator would ignore your average citizen but recognizing the threat of the OWLF would be using every tool available to bring you down. This also comes with the drawback of the player character's "profession". Your average citizen would have a harder time fighting the Predator but would have an easier time escaping it as it will largely ignore the player provided they didn't pick up a weapon. The agent would be armed to the teeth and have to "take out" practically everyone or sneak around the enemies in order to get the Predator but the Predator will absolutely make a B-line for the player. The officer is a balance where the player is armed and can fight the Predator but can be ignored provided the player is able to "sneak" around it.
I imagine a series of checks would work for the Predator to choose the player as the target.
Narrative: Is the Predator in the same place as the player?
Weapon: Does the player have a weapon and if so what kind?
Body Count: Does the player have a body count because while armed the Predator needs to weigh the player's worth.
Profession: If the player is a citizen it will automatically ignore, if the player is an officer it will consider its options, if the player is an agent the Predator will outright be hostile.
The main ideas here is have three possible endings for the three character.
1. Kill the Predator which means killing it before the self-destruct
2. Narrative (a "canonical" scenario)
3. Escaping the town while the Predator is busy
Then thinking ahead here is that for how smoothly a run goes and depending on whether the player got the "true ending" to that story they earn unlockables to make a new run smoother. Completing all three stories with the "true ending" then enables the player to play as the Predator and see what the Predator was doing in-between the stories.