No stereotype is wrong. All of them have basis. The only time it's wrong is when you make the assumption that every member of that particular group fits the stereotype.
For example, I live in Georgia. I do not hunt, fish, eat jerky, enjoy NASCAR, or have intimate relationships with my sister. But I'd be a complete liar if I said that there aren't Southerners who do all of those things. Except the incest. That's completely ridiculous. The same goes for Irish, Scots, Jews, video gamers, teenagers, fat people, white people, black people, Hispanics, every thing else.
Quit crying about how "OMG GAMERS AREN'T FAT, SWEATY NERDS" because there are plenty of fat and sweaty nerds.