I agree. Even he's already in legal age to gamble, the point is, he's still depending on his parents financially and the money given is meant for his studies and not for leisure.
Thus, it's normal for parents to be worried if they became aware that their son is into gambling. Therefore, an advice of looking for a side job is better rather than relying on his mother's given allowance. This way, the son can have a budget if he wants to entertain himself through gambling.
When I reached the age of majority, I could provide for myself, in which case you begin to look at money with a completely different responsibility. Of course, I tried different strategies in gambling at this time, because I was looking for a way to get rich quick, but I did it with extreme caution and worried even about losing small amounts on a loss. So it is possible that when a teenager starts earning money on his own, then his responsibility in gambling will be higher.
Well, that's another way to see it, and I think that you are right and your case repeats in many cases when teenagers have to face the real world when they reach the majority. Unfortunately, not all of them will be as responsible as you were or we may think, and for the parents who suffer something like that it has to be a difficult situation to handle. Because their son is free to do what he wants, and some of them will do the wrong thing. That's why education at a young age is the best prevention.