Both parents' alcohol usage before the child is born can affect the child, and even if the mother does not drink during pregnancy.
But there is certainly a strong genetic component in the disposition for alcoholism. If several generations in succession have problems with alcoholism, this can be either a genetic disposition, learned behaviour from parents to children, or direct metabolic effect of the alcohol on the forthcoming child.
The genetic disposition for alcoholism can manifest itself as a disposition to use alcohol as a method for self-medication. Such people use alcohol in order to cope with various mental and emotional problems and disabilities. Research has shown that people who use alcohol or drugs are more sensitive than others in several aspects, are more impulse controlled, have a stronger need for excitement in life. These traits are similar for alcoholists, drug abusers and also many people with eating disorders.
Note however, that no one is preordained to alcoholism. Even people with such a disposition can learn to handle their life in other, more constructive ways, for example through cognitive psychotherapy.