One shouldn't quit gaming because they're "too old" for it, though there are a couple things which could easily impact one's decision to take an interest in other hobbies/activities/whatever and stop playing games (though preferably not completely so).
Lack of time
Easily the most valid reason to curb one's interest in gaming, because it can be a very time-consuming hobby; hell, MMOs are built specifically to take advantage of this. Most teens don't realize just how time their responsibilities will be until it hits them full force. The standard 40-hour work week might not sound like much, but it's easy to go over that arbitrary limit; while it often comes with overtime pay, there's a pretty good chance any given person will be putting in more than that. With increasing responsibility, the probability for one to go over that benchmark increases as well; as they say, things have to get done. Just as an example, I easily put in 60+ hours a week. And we haven't even touched things like maintaining your home or spending time with family, which is just more time. Spending time playing games seems far less important when you have other priorities.
Moving outside the target demographic
The closest thing to the "too old" sentiment, but it's fairly obvious that people's tastes will change as they get older. Some of the things you enjoyed in your youth can seem far too idiotic or annoying (usually labeled as "immature", but I'm trying to avoid any misnomers) to you when you're older. This is usually the case with trendy or popular games, those which are trying to capitalize on the teen audience. Games which aim to target multiple age groups and don't rely various gimmicks aren't subject to this, but seem to becoming a bit rarer in the current era of gaming.
Lack of time
Easily the most valid reason to curb one's interest in gaming, because it can be a very time-consuming hobby; hell, MMOs are built specifically to take advantage of this. Most teens don't realize just how time their responsibilities will be until it hits them full force. The standard 40-hour work week might not sound like much, but it's easy to go over that arbitrary limit; while it often comes with overtime pay, there's a pretty good chance any given person will be putting in more than that. With increasing responsibility, the probability for one to go over that benchmark increases as well; as they say, things have to get done. Just as an example, I easily put in 60+ hours a week. And we haven't even touched things like maintaining your home or spending time with family, which is just more time. Spending time playing games seems far less important when you have other priorities.
Moving outside the target demographic
The closest thing to the "too old" sentiment, but it's fairly obvious that people's tastes will change as they get older. Some of the things you enjoyed in your youth can seem far too idiotic or annoying (usually labeled as "immature", but I'm trying to avoid any misnomers) to you when you're older. This is usually the case with trendy or popular games, those which are trying to capitalize on the teen audience. Games which aim to target multiple age groups and don't rely various gimmicks aren't subject to this, but seem to becoming a bit rarer in the current era of gaming.