Hmm... I don't think it helps much in this context to worry about terminology, like whether someone is an alcoholic or not. I think it is better to think in terms of whether you have a problem with drinking too much alcohol.
Put it this way though: if someone in their early 20's tells you that they are a heroin addict do you think of them as not really an addict? Would you tell that person that they haven't lost enough to be an addict?