"Charles II, himself a crypto-Catholic libertine, was reputedly appalled by James's folly in matters of religion and sex: 'My brother will lose his kingdom by his bigotry, and his soul for a lot of ugly trollops.'" John Mullan
I agree, Don's drinking is a bad habit, not alcoholism per se. If it were alcoholism he would or should be going to meetings with Freddy Rumsen. I think Weiner is aware of this because he uses Don's drinking as a character flaw, another prop to show his steady decline.