She's not addicted to video games. She has ADD, and needs something that is quick and easy to keep her stimulated, and video games fit that bill. Just when she starts playing its hard to get her to stop. I know she doesn't want to waste the time she has with real people, but I understand how easy it is to go "just another 5 minutes" over and over again.
My apologies, I wasn't meaning addiction as "get checked in to AA" type but just how you explained it. Once you start, it's hard to stop and it becomes the "5 more minutes" problem. I was trying to explain the draw for some people, but perhaps it is only the ADD that is appeased by her gaming.