My thoughts on reading this were that Lissy "needs" to learn to control her language. I'm guessing she didn't really mean those things she said, i.e. she hate you, she doesn't love you, you should go fuck off, &c.
So the question is: What did she really mean? What is the true feeling and thing that needs to be expressed? Saying what you don't mean is ineffective communication.
I doubt it, but perhaps she really does mean the things she says. In that case it would be better to not be in a relationship with her.
Reading the scenario with the computer it seemed obvious to me she was immersed in the game and I know I've been there myself it is a detached place. I have to make it a point to stop playing because esp. if I am having a voice convo and even an IM convo whomever I'm talking to can tell I'm not really "all there" and it's actually pretty insulting.
Maybe a better approach would be to control your own actions rather than to try and exert control over Lissy's. Something like "I can tell you're playing online games right now and I want your full attention. Let me know later if/when you are done playing as I would like to talk to you, but not when you are only half-there."
It could be more or less tactful depending on your diplomatic sK1lz.