I'm sorry you are here. I think you need to turn off the video games, heck, give away the video games. Get a job. She is being very specific in telling you what she needs, and tbh her needs sound very reasonable. And if it doesn't work, then at least you have a job and you have broken your video game addiction.

As far as the anxiety and your mind wandering. Well, that is hard. I think we have all been there. Some of it is going to take time. I am 6 months in and still have my moments. Lots of them. She might be seeing someone, she might not be. Right now that really isn't your problem.

Go for a run, clean the house, clean your car, take the kids to the playground, whatever gets you up and active in a productive way. You have a history of addiction and being left by your spouse is going to rock your world like you will not believe and you have to decide now that you are not going to fall back into bad habits and you are going to come out of this a better person. I hope I don't sound harsh- I know you are in pain, and I truly am trying to find words to be encouraging and to propel you forward. Only you can improve your situation. Think about what you want your goal to be. Keep posting, keep reading, be productive, don't let your emotions and your addictions keep you from moving towards your goals. This is going to be hard. You are in a good place for advice. I wish you the best.