Maybe he would play co-op games with you? Unfortunately, this is sort of a problem that you can't really help with (not concretely). If he's not willing to pause the game and hang out with you, you won't be able to change that; he needs to want to change and right now it seems he doesn't want that or is otherwise overwhelmed by or resigned to whatever's going on.
As someone who also struggles with video game binges that often last 8-24 hours, has he ever considered he might have ADHD? I have it (inattentive type) and depression and what little you've mentioned reminds me of myself.
Even if he doesn't have ADHD and is just avoiding dealing with other issues, looking into some strategies for staying present and managing unpleasant thoughts from an ADHD perspective might help if his main way to cope is distraction. I would also encourage him to see a therapist if he can afford it, but that's a huge step for some and it might take a bit to get comfy with the idea.
Yeah, I thought I didn't have it, either. Then my therapist did a quick informal questionnaire and I scored so high that I couldn't really deny that I should get tested. Just food for thought.