I went through the whole "am I or am I not" debate recently, and I concluded I'm "close enough for government work". For all intents and purposes I am an alcoholic. I may have had an easier time stopping drinking than some people (once I surrendered my personal battle with it), but I know in my case it had been, and was continuing to, progress.
I feel I need more than simply quitting drinking in order to live a whole, happy life, and to ensure that I never succumb to the lure of drinking again.
Ultimately, we each have to decide for ourselves what is needed to recover. What's most important for that, I think, is to be totally honest with ourselves about our relationship to alcohol.