As with most studied, the really interesting parts are hidden in the data.
A few things should be kept in mind. For example, there was a huge difference in two characteristics of the subpopulations. Non-drinkers and former drinkers had much higher incidence of diabetes and being socially deprived compared to moderate drinkers. This is mentioned in the research article but not the Time article. When adjustments for systolic blood pressure, diabetes status, body mass index, HDL-cholesterol, use of statins or blood pressure lowering medication, and whether offered dietary advice were made, the benefits for moderate drinkers decreased but still somewhat remained for some diseases.
However, there was no adjustment for social class. It would have been extremely interesting to see the results with adjustments for social class, or even better just to see the raw numbers for each social class. 30.6% of the non-drinkers were socially deprived ("Most deprived 5th of socioeconomic deprivation") compared to 15.7% of moderate drinkers. That looks like a significant disparity for a characteristic that would seem to correlate strongly with bad health.