I think an addictive personality is genetic, but not necessarily being an alcoholic.
I know an addictive personality runs in my family.
My maternal great grandparents and great uncle all died from drinking related diseases. Maternal grandparents drank heavily but quit completely when they had kids. My mom likes her pills and my dad drank for a while but quit many years ago... he seems to able to have a beer or two now and then so I don't think he's a full blown alcoholic..
That being said I still think it's just addiction that's genetic, not necessarily what you end up addicted to