That article from The Atlantic uses outdated information. The figures Glaser used for AA efficacy do not come from peer reviewed science and are inaccurate. See https://www.thecut.com/2015/03/why-alcoholics-anonymous-work... for a direct rebuttal of that 2015 article.
AA works, but it likely works more because of the community than anything else. Drug addiction is often a symptom of isolation. Drugs often mimic the brain chemicals we get through positive social interaction, serving as a placebo.
You are kind of right. Being a part of a community all going through the same struggle definitely helps. Just not being around people getting wasted is a big help in itself. You can't just take a large chunk of your life away, it must be replaced with something.
The part about helping others is a big factor. It gives a reason other than self, which seems to be a big factor.
It's hard to say what makes it "work" for certain. The Oxford Group, the predecessor of AA, lacked the helping others aspect and did not see widespread success. This is what AA itself considers to be their unique magic.
Or maybe it's all the sayings! God, there are so many sayings.
Despite being very hostile initially, I got a lot of benefit from 12 step programs. It is not something I have stayed formally involved with, but I got a lot of helpful insight.
I don't think any one thing did it for me, it was a long and difficult process. The fact I'm alive and stable today is a small miracle. Most people in the state I was aren't so lucky.
I know what doesn't work though: Shame. I had to stop shaming myself before I could get well.