While there have often been claims of genetic predilections to alcohol/drug dependence there is no actual proof that such a gene exists.
The actual genes do not have to be identified to determine that there is a strong genetic component to addiction, but there is enough evidence to suggest that several genes are involved. Like most genetic traits, however, environment also has a strong influence.
In the case of alcoholism, different forms of genes responsible for alcohol metabolism are associated with different risks of development of alcoholism.
You do not need to identify the genes associated with a specific trait to determine that a trait has a strong genetic component. That determination is made by studies of the incidence of the trait. There are still many genetic diseases where specific genes involved have not been identified.
The first geneticist, Gregor Mendel, did a vast body of genetics research without ever knowing what a gene or DNA was.