Kaskutas,whose 2009 paper "Alcoholics Anonymous Effectiveness: Faith Meets Science" I frequently cite when pointing out that AA works for people who work it, or why early randomized controlled trials did not show an accurate picture of 12-step effectiveness, recently co-published a paper comparing 12-step groups to other mutual help groups entitled "Comparison of 12-Step Groups to Mutual Help Alternatives for AUD in a Large, National Study: Differences in Membership Characteristics and Group Participation, Cohesion, and Satisfaction."
One of the groups they looked at is a no-drinking, no-God fellowship called "LifeRing Secular Recovery." Like AA, they are very adamant about complete abstinence on their webpage: in one article they talk about the "low success rate of Moderation Management, and of individuals trying to moderate on their own," and one of their fundamental philosophies is sobriety, which they make clear means complete abstinence.
Despite this, Kaskutas' paper mentions that "LifeRing [...] members were less likely to endorse the most stringent abstinence goal," which is interesting because stringent abstinence is a fundamental part of the LifeRing program. My take on it, having not read the paper (I am not about to spend 36 dollars getting a paper which will be free in six months), is that LifeRing, and other non-AA mutual aid fellowships, mainly attract people who are not satisfied with AA. My experience working with newcomers is that the biggest stumbling block is the fact that AA strongly suggests complete abstinence for alcoholics; we frequently read a part of the Big Book describing how an alcoholic can never drink moderately again.
Indeed, the majority of people online who are opposed to AA online are people who claim alcoholics can drink moderately; it is not surprising that even an AA alternative which also advocates for abstinence attracts the kinds of people who still think they can control their drinking again.
In terms of the study itself, while showing promising results, it has the same issue that studies which claim alcoholics can drink moderately again have: It is a short-term study using self reported data.