It does work for some people, clearly, but the evidence suggests it's one of the least effective methods.
Your article mentioned that it is impossible to study AA properly because it is "anonymous" so any comparisons to other treatments have to be taken with a grain of salt. More importantly, you can't judge addiction treatment like a black box where addicts are fed in one side and count the number of sober people that come out the other. It just does not work that way. Relapse is a part of recovery so measuring effectiveness requires a longer term outlook (i.e. number of sober days after 1, 3, 5 and 10 years). The author's clear bias against AA was shown by her dismissal of the need to actually "try the program" before it can help. No other medical intervention is judged based on the number of people that refuse to follow the treatment plan. Why should AA be judged by that metric?
More importantly, addiction is a multi-faceted problem and trying to find a single one size fits all solution is wrong headed. i.e. AA cannot help with detox or dual diagnoses (people who are addicts with other conditions such as bipolar disorder). It is a means to deliver cognitive therapy and support to a large number of people cheaply. If naltrexone helps with cravings then it should be used but after 1 year physical cravings are gone and relapse occurs because of a failure to deal with the psychological issues that led to substance abuse in the first place. That is where peer support is invaluable. Who do you really think has a better chance of helping a addict through a crisis: a therapist charging 100/hour who is available 9/5 workdays or a fellow addict that has 20 years of recovery that can be called any time of the day?
Lastly, an abstinence based program is essential to recovery. Telling addicts that they can consume their drug of choice in moderation will generally lead to failure because once under the influence of the drug the addict is no longer going make rational decisions and is much less likely to control consumption. That does not mean that some individuals can make moderation work - it just means that the primary objective of any useful treatment has to be abstinence.