As a 56 year old retired engineer, I've been working with computers and playing computer games since the early 70's. Back then there were no personal computers, just mainframes where you had to use TTY terminals, paper tape and IBM cards. Simple games like Star Trek and others like it were pretty exciting back then because of their novelty and it has been interesting to watch the metamorphosis of computer gaming over the decades.
I have sons in college now and lots of other things to keep me busy but I always make time for gaming. No, I don't play WOW, The Sims or Freecell. I'm a FPS guy all the way. There are a lot more older people out there playing computer games then you think. I agree with the other people here who say there is no age limit for gamers.
I've belonged to several gaming clans with older players and we have been quite successful in various leagues and ladders. I have participated with an UT2K4 Onslaught clan that won $2000 by taking first place in a GGL tournament a few years ago. We also took first place in a XTGL tournament and won six video cards. We entered an UT3 Warfare tournament sponsored by GameSpot and took second place, winning $400. I moved on to a COD4 clan after that and we did quite well in the CAL and TWL gaming leagues.
I'll keep playing computer games for the rest of my life as I enjoy them and I believe the mental exercise they provide keeps my mind sharp and my hand-to-eye coordination tuned.