He drank because of a DnD game that he got anxious about. The fact that you weren't there is really not part of this, I don't think.
There is sobriety and there is recovery. He can be sober for a week or two but he isn't dealing with what keeps taking him back there. If he can't deal with the anxiety from a game, that's an issue he needs to get help with.
Not just anxiety, we all have that to greater and lesser degrees, but he has no coping tools. He has gone through life and drugged himself through the anxiety, depression, celebrations, let downs and social situations. He will have to work on those things while staying sober or this is just a roller coaster ride (for both of you).
Do you wonder if the couple of beers a night is true? There is something wrong with this scenario. Why would he be ashamed at the DnD game, they don't care if he drinks. Why drink 2 beers a night, there is no comfort or buzz in that. It just doesn't add up. That said, I could be wrong.