The study is suggesting that the heretofore observed beneficial effects of moderate alcohol consumption (the "J" curve wherein there appears to be a "sweet spot" for health benefits at moderate consumption levels) may be greatly exaggerated thanks to selection bias and failure to account for confounders in prior studies.
That is, the benefits of any alcohol consumption may be greatly exaggerated (if not completely nonexistent) for most of the population.
The BMJ has an editorial on this topic[0] which is entitled "Alcohol’s evaporating health benefits" and refers to this study (I figured people on HN would be more interested in the study itself). That editorial heavily implies that the prior (potentially flawed) studies received widespread notoriety due to the alcohol industry's media influence.