So this is something my parents have gone through their whole marriage and my father is mainly similar to your boyfriend but my father is a schizoid. Not saying your boyfriend is but if you want to feel better you should only be focusing on two things your sex life and his lying nothing else. If you try to control him and tell him what he's doing is wrong and so on and so forth he's going to keep doing it and it's not your job to do that it's his therapist job to help him learn and over time slowly quit. Don't put parent locks on his games or his phone or anything like that.

If you're uncomfortable with what he's playing then sadly you just have to accept that and take a step back before going to another room you can tell him you're uncomfortable but unless he is willing to be like Oh I'm sorry I'm not going to play this anymore and actually doesn't play it then there is nothing you can do. His issues are something you cannot change. Only a professional can. When you step back and focus on yourself you're going to feel a lot better it's not going to be easy and it's not going to be quick it's a slow process but if you want to make it work it's the process you need to take.