I think there might be some kind of genetic trait (traits), that generally make people more predisposed to any kind of addiction. Thus, certain people with a prevailing portion of such genes can have bad self-control and better stay away from both gambling and alcohol. On the other hand, others can control themselves perfectly, and no amount of gambling or alcohol will lead to addiction.
I don’t think one thing can lead to the other, it’s rather a person that easily becomes addicted will become addicted to anything he/she is exposed to.
In addition, environmental factors play a role, such as parenting and a circle of close friends, that form our behavior.
To support my idea I’ll provide an excerpt from
an article by Harvard which states that certain genes may be involved in drug addiction:
Drugs of abuse, including opioids, act on the brain’s reward system, a system that transfers signals primarily via a molecule (neurotransmitter) called dopamine. The function of this system is affected by genetic and environmental factors. For example, a recent study published in the scientific journal PNAS revealed one of those genetic factors. Researchers demonstrated that a type of small infectious agent (a type of RNA virus called human endogenous retrovirus-K HML-2, or HK2) integrates within a gene that regulates activity of dopamine. This integration is more frequently found in people with substance use disorders, and is associated with drug addiction.
While it only provides information regarding drug addiction, there’s a reason to assume that similar factors may stand behind other addictions as well, since the above-mentioned genetic factors impact the whole reward system, and the latter is known to play a crucial role in all types of addictions.