That situation sounds fairly familiar to me. I'm sorry to say that in my case it ended up with a divorce, but maybe you will fare better.
Something's broken in your relationship and if you want to keep it, there's work to be done.
He might be escaping into his online gaming because it's the only way that he feels like he can enjoy being at home. When my marriage started feeling like we were just running a business called Our House Inc., and all of our conversations were about that instead of having any kind of fun together, I stopped wanting to spend time with my ex. I used to go and talk to my friends in a pub, your fella is playing computer games.
I notice that you ask him to do things as a family and he turns you down, so now you don't even ask. Do you suggest date nights for just the two of you? It may be time to show him what damned good, fun as hell, sexy girlfriend he has.
You can't just go straight to having sex and thinking that'll fix everything. Sex with someone you don't really like spending time with isn't loving or particularly fun. It's mechanical and probably makes you feel worse rather than better.
But let's say you and he have just come home from a great night out together. The kid is staying at your parents', or his parents', or your sister's, or whoever you have.
You've dressed to wow him, flirted with him, made him laugh. Then you get back and he knows he's brought home the best girl in the room. THAT's a good time to initiate some intimacy. Change the location in your house where it happens, change some other details (not going to go into detail, you know the sort of thing I mean) - make it exciting for both of you.
Try to have conversations that aren't about the house, the child, money, jobs that need doing, or the state of your relationship. Those are all conversations that can seem stressful. Have conversations about things that you might talk to your friends about. Make him see that talking to you can be a pleasant experience and not always a Big Talk. He might start looking forward to talking to you instead of dreading it and hiding in his online games.
When you've done all that, you'll have every right to expect him to reciprocate the effort. So if he doesn't, tell him that you'd like him to. It doesn't have to take an hour and you don't have to list all the changes you've made to help your relationship. Just say that you're making an effort because you love him and that you hope he'll join you.
Hope something in there was helpful.
It's hard to say what is going on with him. Would he be open to couple's counseling? NO, absolutely don't go out to meet other people to find out what you need. That makes no sense. Even if this ends, you shouldn't date right away. Take some time to figure things out on your own. good luck