Here are my thoughts CN.
I drank for the best part of 20 years and sober for 5+. I drank my life as I knew it, slowly into the gutter and I was the last to see it.
Does it really matter at the end of the day if he 'admits' that he is 'alcoholic'? If he recognizes that he can't control his drinking and by staying quit he sees that he will be more healthy, can lose weight, save money, won't get into trouble around alcohol, (that's a biggie) no more hangovers... what difference does it make that he use the word a.l.c.o.h.o.l.i.c. I think he recognizes that alcohol is a problem in his life and that not one thing he associates alcohol with is positive. I wouldn't push for naming himself and let him continue the process of staying sober.
None of us know what is down the road for us. There are no guarantees in life for anything. You will deal with whatever presents itself if and when it does. Today is all we know what to do with.