If someone wants to train their mind, they can still go for other mind games that doesn't actually require them to gambling with real money, some people can feel convinced that gambling can train their mind but once they dive in, it becomes a different story entirely. I don't disagree with you that gambling is a mental sport but in the way you described it, it's result will be different for every individual, it can only be used like that and would prove positive result in some individuals but for many people, you will get an opposite result since they would have a biased thought, not to stretch their mind again but to make money from what ever game it is.
Though gambling might be referred as a mental sport that may involve the mind on certain games, but actually depends on individuals. As for me, certain game play or sport betting could just be for the fun irrespective of the fact that real money was used to stake them. I personally think that certain games is a big time fun whether they are mental sport or a form of gambling, it may be irrelevant in my opinion.