My father was in AA and sober for 32 years before he died last year, had not had a drop in that long. He would have certainly defined himself as an alcoholic, even though he had been sober that long.
My opinion on this is skewed because of my personal experience, but I'll tell you this, the only person who can tell you if you're an alcoholic is yourself. If you don't think you are, you aren't if you do you are. It's really that simple.
Now you might say, "what about the person who is ruining their lives, and killing themselves drinking, but doesn't think they're an alcoholic?" Until they realize the addiction they're a drunk, and that's a fine difference. A drunk is just a slow suicide, an alcoholic is an addict who is potentially empowered to change themselves.