The hell? There's no age-gate for anything. Except maturity. If you think someone enjoying something is childish, instead of feeling happy for them, then you're the one who has growing up to do.
Books are also a great hobby, which many find boring, but it's never considered an age thing just because the typical adult isn't into reading books. The same goes for games. Not everyone enjoys them, but that's a matter of personal taste, not age. Sure, our tastes can change during our lives, and some people "grow-out" of their childhood interests. But that might be more correlation than causation.
Take my dad, for instance, I remember him gaming on his PC and PS1 during my pre-teens, but he stopped gaming for many years. But recently, he got BACK into gaming, and asked me to build him a modern PC to play on, since it's been so long since he's used non-apple computers. These days, when he finds the right type of game for himself, he is more difficult to get away from it then I am.
Games are a new medium, and new things get adopted first by new generations. So maybe older ones consider them a "kids" thing, but at 26, I see no reason why video games would ever stop being a part of my life.