A gamer punk is a person who generally plays video games, but has a punk attitude or clothing style. Gamer punks normally are the more popular of the gamer stereotype, not being very nerdy. You could find a group of them hanging out at an arcade or a gaming center, wearing punk clothes.
Person 1 "Hey, look at that gamer punk over there."
Person 2 "Is he playing World of Warcraft?"
Person 1 "Yeah, hey, he has a lot of piercings. He's wearing a Ramones t-shirt too."