Effectively, the inverted U-shaped relationship means that heavy drinkers have lower earnings than moderate drinkers. It is easy to see why this would be so, due to the negative health and productivity impacts of being a heavy drinker. However, it also means that abstainers (those who don't drink) also have lower earnings than those who drink moderately.
There are several reasons that are proposed for why this might be. First, there is also an established literature that demonstrates a J-shaped curve of the relationship between drinking and health outcomes (Eric Crampton has many posts on this topic, but this one from 2010 is a good place to start). Moderate drinkers have better health than abstainers, so perhaps they have higher earnings because they are healthier than abstainers. Alternatively, perhaps there are positive networking effects (or improved social capital) associated with moderate drinking. Engaging in moderate drinking with colleagues and peers allows workers to deepen their social networks, allowing them to improve their earnings by having access to better jobs over time. Or perhaps the socialising allows them to signal their commitment to the workplace and their colleagues, which improves their chances of successfully receiving promotions or pay rises.
Srivastava uses data from the 2001 and 2004 waves of the National Drug Strategy Household Survey in Australia, and her results are that:
...an inverted U-shaped relationship is found between drinking and earnings across both male and female workers, with a premium for non-bingers and occasional bingers over abstainers, and an earnings penalty for frequent bingers.The paper is a little questionable (for technical reasons [*]), but for me it left the biggest question unanswered. Is the wage premium for moderate drinkers a result of better health, or better social capital? This is an important question, because workplace drinking and after-work drinks are becoming less common over time. So, the relationship between drinking and social capital is plausibly weakening over time. So we might expect that, if the wage premium for moderate drinkers is primarily driven by health, the premium would remain robust over time, but if it is primarily driven by social capital, it will probably be declining over time. This is an interesting research question that, as far as I can see, no one has yet adequately addressed.
[*] I also take issue with Srivastava's choice of instrumental variables (for more on instrumental variables, see my post here). She uses three instruments: (1) the price of alcohol (at the State level, which means only six observations for all of Australia, so this instrument is actually dropped from the analysis); (2) whether the person first smoke marijuana before age 16; and (3) whether the person has a tattoo. Instruments are supposed to affect the endogenous explanatory variable (in this case, binge drinking), but not have an effect on the dependent variable (in this case, earnings). However, people who smoke marijuana at a relatively young age or who have tattoos might be less risk averse, and less risk averse people may invest less in human or financial capital (e.g. see here), leading to lower income. So, it isn't clear to me that any of the instrumental variables are valid.