No, NH isn't particularly a state of alcoholics. What is seldom talked about is that NH makes liquor sales a state enterprise and keeps prices low to build volume. Headed north from MA, the first NH exit on I-95 debouches directly into the parking lot of a very large state-run liquor warehouse/welcome station, much patronized by thirsty Bostonians and other residents of high-tax MA.
NH attracts customers from ME, MA, VT, and maybe RI, CT, and Canada, to patronize their state stores and buy cheap brand-name booze. The other states wring more taxes out of liquor sales, so-called "sin taxes" while NH emulates Walmart, sells it cheap and reaps big profits.
NH sells 4.67 gallons of alcohol per capita but doesn't drink anywhere near that much. Maybe half of that is drunk by residents of other states and, for all I know, provinces. The following is from their website:
Over the years, New Hampshire residents and those from surrounding states for miles around have chosen to shop for their wine and spirits at our conveniently located New Hampshire Liquor & Wine Outlet stores. This has not happened by accident, but by design, as the State Liquor Commission aggressively pursues a strategy that provides you with the best possible value and the most pleasant shopping experience.