Quoting MX23:" i dont agree with you if she doesnt start having sex than he could end up cheating but doubt he is now."
Threatening to cheat is not the way to obtain sex from a woman. He could be the one cheating for all we know. A good way for him to get sex is to 1) stop playing video games and play with his son. 2) Compliment his girlfriend on how attractive she is to him in a positive light. 3) Stop being a man child.
OP, I'm so sorry you have to deal with this. You do not deserve to be treated like this and accused of cheating.