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.
I don't think so.
Playing mind games without gambling is more about improve your skill because you're not under pressure.
But, if you play mind games and gambling, it make you play with a pressure because if you lose, you will lose your money, this will affect your mental.
Remember that the idea of this is still to strain our mind a little or should I say the essence of it is to quicken our mind and not to put it under a bad pressure of losing money. Whether you gamble with real money or not, there are still some mind games you will play and you will get that same desire of exercising your mental state, you don't have to stake with a real money first before you feel that you have exercised your mind.
Like you said that if we play with real money, it makes us be in pressure because of the lose of money, that doesn't only work with money. Try playing chess, try playing some video games against your friends, try playing some word puzzle games that has a few minutes or few seconds timer and you will feel that urgency to win and not to be defeated.