I do think you are right, they start out on gameplay; getting that inner game loop to be fun is primary (I kind of though that's how most (non narrative) game studios worked though).
they don't make games to tell stories
This was mostly what i was suggesting was incorrect. I also don't think it's a major part of marketing. I'm suggesting they don't bother putting the work of story into something until that inner game loop is fun.
TF2 was the result of experimentation with team based death match gameplay
Didn't they already know about team fortress? This seems off based on team fortress having already existed, same with wolfenstine enemy territory.