A hard-drinking person drinks a lot of alcohol, regularly, not just at one party. The word describes a habit. You will see it in profiles of musicians, writers, and old film characters. It is not a doctor’s word like alcoholic, and it is not always meant as praise — though some people say it with a kind of rough admiration, as if heavy drinking were part of a wild, hard life. “Hard” here means “heavy / serious,” the same flavour as hard liquor, not “difficult.”