People still enjoy 50-year-old movies. Why is a video game necessarily "expired milk" just because it's five years old?
The games industry makes their money on game sales, so they want customers to purchase something new and not play something that is five years old. People do in fact play old games, some even are new customers paying for these old games via re-releases or emulation from gog.com (formerly Good Old Games), Nintendo's Virtual Console, or any of the other digital distribution services. It does happen but it is not the norm, nor what the games industry, and certainly not the triple-A game makers, really wants.
1. Playing games is time consuming. Where the average movie may clock in at slightly over 2 hours, most games require ten times that much time. In fact, some gamers demand that a game occupy their time for a certain length or they feel that it's not a good value. These people are a problem too but that's another story. Games also require more of the user's attention. You can have a movie on in the background, and maybe even be having a conversation about it. For the most part games require significant more concentration by the user in order to be completed.
2. Playing games requires a higher cost of entry. If you purchase a cheap $20 DVD player, you can watch practically any movie released on the format. (yes there are region coding issues but anyway...) And since Sony was able to finagle Blu-Ray to be the de facto standard, purchasing a cheap $60 player will let you watch practically any movie on that format as well as the ability to play DVDs. Contrast this to console gaming where someone would have to purchase a specific console if they want to play an exclusive game, or if it's a PC game, have one that meets the minimum system requirements. These are more complex than the "purchase disc, put disc in player" that even your grandparents can perform.
3. Video games have their opening month where they make the most money for the publisher. This is the closest thing the industry has to a theatrical release. When they start being traded in to the second hand shops, the price starts to fall and the major money making starts to slip. This is why triple-A titles are trying to go for a long tail sales period and sell DLC to extend the life of the game. This unfortunately means that points 1 and 2 are made worse by the publisher trying to make money. It also leads into...
4. Video games, or at least newer ones, are ephemeral. They are more and more reliant on hosted servers and active player bases in order to simply function. This point alone makes the "expired milk" comment simply due to the fact that once a game is unsupported by the publisher, it is no longer playable. In some cases, games that could be perfectly playable otherwise have been removed from digital download services and are no longer available for purchase.
Any time that a publisher is selling you an old game, it is either as shovelware or due to the fact that they are banking the nostalgia to sell you the latest version... or in some cases it's because they have such a small lineup of games for their new console that they have to bank on Earthbound which could have easily been also ported to the previous console but hasn't because they are trying to move stock... but I digress.