My very first experience of online gaming was in about 2003 when I picked up a cheap copy of Microsoft's Combat Flight Simulator at around the time I got my very first internet connection. I clicked on the "Play it on the ZONE" button and within a couple of days had been kind of "adopted" by one of the clans ("squadrons" in the world of online air combat sims). They guy who ran it was in his late 70's, and one of the most active members.
In fairness, he didn't actually join any games that weren't purely intra-squadron, and the odd inter-squadron arranged game. By his own admission he wasn't always able to keep up with the "young guys", although I find in general there are not many kiddies in the world of online flying, and the ones there are tend not to be of the potty-mouthed XBOX Live variety. Most players are anywhere between their early 20's and late 50's.
Without wanting to generalise too much, I think that the nature of the gameplay - long periods of inactivity and managing the aircraft systems, combined with a few frantic moments of adrenaline pumping combat, closing with an opponent at hundreds of miles per hour, then trying to keep track of everything going on in a 3 dimensional battle space - appeals to a type of gamer who was brought up with games that were often more complicated and sophisticated in pure gameplay terms.
I don't think you grow out of gaming. You just stop being mainstream. Today's mainstream fashions and trends in gaming are tomorrows niche market. A lot of people stop for other reasons; it's hard to fit gaming around a family and a job too, but I don't know anyone who ever stopped because they thought they were too old.