I'd like to tell him I think he is an alcoholic and I have no room for that in my life and I don't want to be in any kind of relationship with him.
That sounds good...I might suggest not actually saying you think he's an alcoholic. Maybe just say that he drinks more than you are comfortable with and you don't want to be in a relationship with someone who drinks so much. Either way would probably be fine, but he could argue about the word "alcoholic" whereas he can't argue that he didn't drink a lot because you were there to see it.