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https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2746426/That article shows that people who regularly go to AA meetings are more likely to be sober (e.g. 67% people who went to one or more meeting a week were sober 16 years later).
Because of the universal nature of AA, it is hard to randomize for it (if you just randomly tell an alcoholic to go to AA, they have already been told that by others, so that's not a very good randomization; the control is contaminated); that said, there are studies where people randomly selected to go to AA are more likely to be sober. A 2014 meta study shows that greater AA attendance results in greater sobriety, which can not be attributed to self-selection (in other words, we have finally scientifically demonstrated that the people doing well are being helped by AA):
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4285560/
Now, that Gabrielle Glaser article you link to which claims AA is a cult uses some very dubious figures for AA's success. They come from Lance Dodes; since Dodes could not find any studies that AA has a 5% success rate, he instead multiplied multiple numbers from unrelated studies to synthesize the 5% figure. His numbers have been questioned by a number of treatment experts, including Thomas Beresford, John Kelly, Gene Beresin, and Jeffrey D. Roth (who called Dodes's figures a "pseudostatistical polemic").