I take it you didn't like Indigo Prophecy? Since, you know, the second half of your paragraph is the game's ending. Spoiler to the two people who still cared, five years (and four pages) in.The other noteworthy thing about the story in Left 4 Dead is that there isn't much of it. There is exactly as much as we need for the game to work, and no more. Once the particulars are set up, the story doesn't keep shoving itself to the forefront and getting in the way just for the sake of trying to be like a movie. The designers didn't put in an ongoing plot where you chase around some mustache-twirling idiot of an antagonist who engineered the entire zombie plague and now wants to kill the survivors to complete all the items on his "clueless villain" checklist. They didn't put in some "obvious traitor" side plot. No global conspiracy. No author-insertion mystery oracle to deliver exposition. No awkward love story. Nothing about saving your parents / children / significant other from the threat. The story is small, lightweight, and packs enough punch to set the mood and tone for dozens or even hundreds of hours of multiplayer zombie-smashing.
I feel like David Cage would really benefit from a "less is more" mantra.