Hello and welcome!
Phew, I read through your post and will probably have to reread it to make sense of it all but just a few quick observations:
1) Most people who describe themselves as being in a polyamorous life situation at least cuddle with their paramours. And cuddles and kisses often lead to something more. Hoping to have an entirely chaste poly dynamic probably won't work for any extended period of time.
2) Your wife is addicted to gaming. Is she getting help for her addiction?
3) Your wife is repeatedly cheating on you with multiple partners, and chooses to keep on lying to you. How educated is she on poly? Her behavior towards you, in my opinion, is closer to emotional abuse than anything that could be described even as struggling polyamory.
4) Final question; What at this point in time is your greatest motivation to continue your relationship with her?
Me: bi female in my twenties