Gambling is already considered as a metal illness by some psychologists, but who cares. Gambling itself is a form of entertainment, addiction is a separate health issue.
It's kind of crazy for doctors to say that you have mental illness just because you are gambling. Most gamblers can still live a good life even if they gamble every day. Just like a person that use cigarette in order to relieve stress, gamblers also just do gambling to relieve their stress. Some gamblers use casino as their place to hangout and socialize with other/new people which has the same interest as them.
If you are sick of gambling then looks for a doctor or a psychologist that can help you with your gambling problems and they will be able to help you into getting rid of gambling for good.
IMO, psychologists might be able to help you just like a drug addict need a rehabilitation. But the only person that can cure you from your addiction is yourself. Without your cooperation, the money being paid to the doctors will only go to waste. Some people even just discipline/train themselves to not gamble and they eventually completely get rid of gambling. It's a matter of willingness to quit gamble and how much you can sacrifice to do so.