Two things come to mind..
--A teen who plays games and this activity is internalized so the teen becomes a GameTeen (as opposed to, say, a SchoolTeen). In other words gaming becomes a major trate of the teen. A site then could be about this type of "lifestyle" or stage.
--A game played by a teen. However, this should correctly be "TeenGame". In any event, there may be games other than eletronic games played by teens and "gameteen" may refer to any such game (with the limitation of reverse wording).
What do others think when reading this?