I think alcoholism is better classified as a substance use disorder as classified by the DSM-IV.
BehaveNet® Clinical Capsule™: Substance Dependence
I also believe that a personal desire (i.e. willpower) is essential to overcoming alcoholism. It may require help or it may not. Some can combat this on their on while others cannot. Nonetheless, sobriety is for alcoholics who want it, not need it. There are plenty who need it, but never get sober.
Perhaps, you are not an alcoholic. Only you can say. However, you are choosing abstinence and are posting on this forum. Maybe you are a problem drinker that has the occasional control issue and his drinking has led to some negative consequences in life or maybe not. Perhaps, you never experienced waking up one day and being so resolved to stop drinking, then the hamsters start running around their wheel in your head. The next thing you know, you are drinking, even despite your best intentions. And every drinks keeps that mental obsession going.
If you have control over that, then more power to you. I certainly don't. The only thing I have any control over is staying away from the first drink and sometimes that requires help. Initially, that required a boatload of help.
I have no problem saying that I am a pickle and realizing that I will never be a cucumber again.
Regardless, Congratulations on your 51 days! That is most excellent!!!