Many people find it difficult to accept who they are and the bad habits that they have, accepting a habit is the first step that will determine if any help offered to you will work. As a gambler, will you find it offensive if you are referred to as a gambling addict? will you easily accept it or try to give excuses like some other people do, saying that they are not addicted to gambling when the signs are clearly there. Do you think identifying as an addicted gambler will make people stereotype you. The answer is different for every gambler here.
It depends whether you're mentioning it to them in private or doing it publicly, if the intention is just to make them realise that they are addicted we should tell them in a way that won't embarass them but if just want to do it public then the intention is just shaming them which is not appreciated and going to drag you issues further.
Encourage them to seek professional help by letting them know there are ways to overcome this addiction but if someone doesn't want to acknowledge or accept their addiction, it is not your responsibility to force them to do so. You can offer support and resources, but ultimately it is up to the individual to decide.