I never think that you're too old to play video games, and with some studies saying that video games help stimulate the minds of older players, it could actually be healthy to play them. Now, I don't think that retirement homes should start having Call of Duty parties, but simple things like Wii Sports (as seen in the picture at the top) can keep seniors both active and happy, so if they're having fun, why should there be a limit on how old you have to be?
In fact, there are a few older people in my family that are in their late 60's/early 70's that really enjoy puzzle games and things like that on the computer. I don't think they would ever get into console gaming, but it wouldn't surprise me if our generation are still playing some of the newer things well into retirement.