People will give you different definitions, but for me, I always thought that a person is likely an alcoholic if something like a mental "switch" goes off after the first couple of drinks, to where they are then set into a "spell" of unstoppable binge drinking from there on out. This continues until they pass out or become as "high" as time/money allows. This "spell" completely takes a hold of the person; perhaps negative behavior will arise, but it does not always (in fact, for many "functioning" alcoholics, it often doesn't) - the most central characteristic of this "spell" is just that it renders a person utterly incapable of stopping once started.
So to me, alcoholism is not defined by the negative consequences of drinking -- rather, it's the way of drinking itself; the mental obsession, the inability to stop.