To go into it a bit further as I'm just home from class and have more time, alcohol addiction is a pretty serious disease that can have major impact on not only the physical and psychological health of the addict, but also the emotional, and often physical and psychological if the addicted is abusive, health of loved ones.
I would say the man is quite possibly within the definition of an addict, especially if he continues to use despite consequences. Perhaps he's still at the stage where he's able to hold it together and thinks he's hiding it from most people, but I feel like his treatment (id est, disregard) of Bingo's repeatedly-stated concerns is telling and makes for a patently unhealthy relationship.
He needs treatment. I'm not sure what kind of addiction treatment they have in England, but it can't be much different than what we have in America; some form of a Twelve-Step program would be excellent, as long as he gets a sponsor and actively works with them to combat his disease, otherwise he is not really in treatment and is not going to stay off the booze for any significant period of time.
Unfortunately, as with most addicts (especially alcoholics), this man does not feel like he has a problem, and often times, there are two ways addicts realize they do have a problem, those being when they hit absolute rock bottom and have that epiphany in the mirror one morning when they realize they're killing themselves and ruining their life and the lives of their loved ones; or, when their loved ones create consequences for the actions of the addict by leaving and severing contact with them until they have made significant progress in the treatment of their addiction (not just empty promises to "stop" or "cut back" because addicts lie, and that's the blunt truth). In either case, it is unfortunate that it has to reach such an extreme point, but those are really the only ways: you can't change someone who is unwilling to change, and the addict must be willing to seek and commit to treatment.
