[Intrepid Homoludens]

In the case of a FPS whatever story is being told, no matter how integral, serves to provide context to the action (shooting, killing, surviving one level after another). It simply makes the entire experience a bit more interesting, it helps deepen the world you're in, adding to the immersion and hence the enjoyment.

Historically, in a 'typical' adventure it's the story that serves as the nucleus, the primary motivation for players to forge ahead. Whatever else happens to be implemented - interactive items, conversations, puzzles - serves this.