Need to vent

So my baby is one month and 2 days old. My boyfriend and I take shifts watching him and taking care of him. Well while my boyfriend is taking care of him he plays these dumb games that if he leaves the game for any reason he gets banned (and I mean any reason his sister was being taken to the hospital and he told that to them and they still banned him) so I'm pretty sure he's putting that dumb game before our son (and yes I have asked him multiple times not to play it while it's his turn, but he does anyway) and it just makes me so mad! And he puts this game before me ALL the time. Anyone have any advice on what I should do or say that will get through his thick skull to NOT play that particular game?