Wow - goosebumps - this sounds exactly like my relationship, and my A, except I am the one that ended it. We've had the same conversations, and are in the same position, except we do live together. When I ended it, he flipped out mad, came back 2 days later and vowed to quit drinking. He quit for a month (maybe?) then said he could drink like a normal person. He has a few beers a week (that I know of,) never gets drunk (that I know of,) and it has been 3.5 months since he made that bs promise to me.
If I had stuck to my guns, I would be 3.5 months into my new life with HALF of the pain of alcoholism that I currently deal with (my boss is also an A - that's fun...)
Anywho - he didn't quit, alcohol still feels like the most important thing in his life, AND I get to deal with the mood swings, depression, and distance from him because he is not drinking nuts out like he wants to be. And I am just waiting for the day when he says F it, I don't care, and buys his first of the next thousand half gallons of cheap vodka again....
As others said, don't be surprised if he calls making promised and begging you back - I NEVER thought my A would do that, but he did...and I fell for it against my better judgment.
He did you a favor - you will be SO much better off. A's are not perfect for us, they are not our soul mates, and they will not give us the happiness, or reciprocal relationships that we deserve. (((HUGS))) I empathize so much with you.