The amazing thing about Left 4 Dead is that it manages to focus almost exclusively on the mechanical 'gamey' parts while still relaying to the player the larger narrative, while still world-building. One might say that this is a sophisticated manner of telling a story in a game: it isn't forced, people who aren't interested can ignore it, and those who appreaciate narrative can dig in. Everyone wins.
Actually pulling all that off isn't simple, else we'd have less games that fumble with their narrative. But in a Gamasutra feature, various developers described the ways they did exactly that. Valve in particular explained their approach as
"For campaign specific lines, we go through the maps and mark up areas for the players to mention or to talk about. We can control the chance of them speaking when they see it and how far the player can be from the object before they speak. So for the maps of The Parish, if you get Coach close to most signs and look at it — he will often read it. Other times you will notice, characters will talk about a plot point — these bodies don’t look infected — when they are in a general area.
"'Clever' lines can become tiresome if you hear them too often, but if you choose to only have Nick make a comment about his suit while in one map and only 10 percent of the time — players won’t become irritated by the line. We also always make sure the characters are saying something, if nothing else at least, 'reloading'. This gives a bed for all the lines to live in and become part of the world. That way the story points don’t stick out of the silence."
This design, coupled with the AI director, makes it possible for Valve to write for a game where replayability is high. That's not an easy feat.