Are you by any chance a teacher in real life? Because you're sure starting sound like one. Your point is either that there is no such thing as "the stereotypical gamer" or that I applied the word "stereotype" incorrectly. Either way, you're probably right about both so I'll rephrase by saying this: most people are not inclined to assume that a 48 year-old woman plays video games in her spare time. There. Nothing wrong with that sentence, I hope.
I wasn't trying to be corrective, just making conversation so don't take it the wrong way.