I think when most people think of "too old" it's the sort of thing the OP mentioned - Jobs, family, career, etc.
Physically I don't think you can be too old to play games. If I recall correctly there was a dude playing Legend of Grimrock with a *mouth* controller due to paralysis. That's hardcore. If that doesn't stop you, the numeric year of your birth certainly can't.
As far as the "get a job, etc. etc." thing, it's not that you necessarily *have* to stop gaming, but you do have to seriously adapt your habits. There are time constraints like a job, family, spouse, kid(s), etc. of course, but there are other things to work around.
The thing you have to grow out of isn't gaming, but insistence on the self-appointed right to do it "whenever you want." That's the awesome thing about childhood when you get right down to it-- provided your parents weren't abusive, hardcore pricks, you have just a bit of indulgence to be selfish. To be insistent about your hobbies be it gaming, baseball, rocketry, etc.
As restrictive as school and chores and parents may have seemed, they weren't a patch on the interference that life throws at you. Just keep gaming, keep working, keep family-ing and friend-ing and keep enjoying life.