Genes and environment both contribute. It’s not one or the other. Think of the genetic component as an inherited vulnerability — a predisposition. The more vulnerable you are, the better your chances of becoming an alcoholic. The environment can increase or decrease those chances.
Of course, you can become alcoholic even if you have no family history. But you’re at lower risk.
However, there’s probably no single gene that causes alcoholism, and no genetic test to determine an individual’s risk. Most people just look at their family history. If there are many alcoholics in the family tree, that suggests elevated risk.
You can sketch your family history to get an idea of the prevalence. Unfortunately, families often hide problem drinking from the younger generations, so there may be a few skeletons you don’t know about.
As far as skipping generations, that’s common even in disorders that are related to a single gene. It has to do with dominant and recessive traits. The science-minded might want to check this far more detailed explanation.
Alcoholism is a very complex disorder, so it’s easy to see how, without the right environment, it might skip a generation and show up in force in the next.