One of the claims the paper was investigating was that 1 drink a day was better for you than zero drinks a day, and for that they found no evidence. They're not saying that a drink a day is significantly worse than not drinking.
Except that is almost certainly not true and not backed up by this study. The study set out to find the number of daily drinks of alcohol that minimizes health risks, and found that that number is zero. What the paper states is that increasing your alcohol consumption will never lower your health risks.