The study you linked says that for a certain measure, it works better according to a grand total of two studies they looked at. For the rest, the conclusion was that AA performed as well as other interventions. It's also a review study, which can sometimes be helpful, but often cannot draw clear conclusions due to the studies being reviewed not necessarily measuring the same parameters. They also rejected about half the papers they found due to apparent bias.
It's certainly not the kind of paper that establishes something as settled science and even at that, it doesn't say what you claim it does.
The purpose of my comment was refuting that 12-step programs aren’t science-backed, which is blatantly false. As you’ve stated, the entirety of literature on the subject shows that it’s at least as good.
You'll want to reread your study there. For most of the criteria they measured, the conclusion was that AA performed as well as other interventions. Not better. It certainly doesn't establish AA as the superior treatment. The author's conclusion seems to be that it might be about as good and it's free.