People still enjoy 50-year-old movies. Why is a video game necessarily "expired milk" just because it's five years old?
They're not always, but remember that many games don't have much of a story beyond a basic framework designed to push you through the various parts of the game. When a newer game comes along in the same genre, the old ones tend to be left behind unless they had something that made them important.
The original Wolfenstein, Doom, and Duke Nukem will probably be played forever since they were the defining titles of the FPS genre. The most recent releases in any of those lines, probably not. Need For Speed 3 showed the world that running from the cops was something we all secretly wanted to do in a no-consequences environment. Its official sequel in the twisty Need For Speed line, Hot Pursuit 2, is all but forgotten.
Multiplayer can play with this in both directions, lengthening the lives of some games while shortening others. A shitty game with fun multiplayer, particularly if its cheap/free/easy to pirate, can live on for years as long as the servers stay populated. A great game that's been abandoned by its players for something else, likewise, can die off rapidly. There's a critical mass required for multiplayer to keep the game healthy, and that's where a player who's just looking to play can find a game that roughly approximates what they wanted to play with enough other players to actually enjoy it. Fall below that level and you quickly enter a death spiral as those who are still playing find themselves more and more often without a game.
Basically in 10 years I still see myself firing up Halo or Borderlands if the hardware available to me allows it, as I liked the story. The existence of sequels or "better" titles in the genre doesn't matter, since they won't be the story I want. That's comparable to a movie.
I probably won't, however, be firing up Forza Motorsport 3. As a sim title with no real storyline beyond completing a set series of races for a "Career", FM4 improved upon it in all ways leaving no reason to back up.