None of that sounds (or looks) traditional, but I'm glad someone sprung for the inverted Mexico Filter for this game. (That weird tint is really detracting from the visuals.)
For what little value my opinion lauds, I tend to think of a traditional FPS as a person (of unspecified appearance, Ageless-Faceless-Gender-Neutral-Culturally-Ambiguous-Adventure-Person. AFGNCAAP, but replace "adventure" with "Shooter".) and their shotgun.
No squads, no story, no future; near or otherwise. 1-6 weapons at most.
Half Life, for the innovations it did bring to the table, is closer to a traditional FPS once the tram ride is over. You don't make any major decisions, you are funneled though a majorly linear set of distinct levels/areas, and anyone who joins up with Gordon is ephemeral and likely expendable, too.