The concept of gambling as a form of mental sports refers to the deployment of mental strength in some skill-based games and without physical display of strength or fitness.
Games like Chess, Blackjack, poker and even Sports betting fits in this criterion since professionals employ some good strategies, calculations and even critical analysis before taking the decision on your next line of action. These mental involvements stretch your mind and success in them is a product of strategy, constant practice, psychology and accurate decision under pressure.
Of course, gambling is a form of mental sports, especially the examples you gave, but Sports betting is actually a doubt to me.
Yeah, i agree that they all require skills and proper understanding, but sport betting uses a large percentage of luck considering the fact that you as a bettor don't necessary influence the game, which is unlike Chess, Blackjack and Poker that you can influence the game more with your skill and level of thinking. You can actually be a master at Chess, Blackjack and Poker, and dominate for a very long time, but sports betting isn't like that even if you have that mental skill to make your own analysis.
I personally respect those that are very good at Chess and Poker games. I see them as extraordinary individuals, because of course, it takes good mental skill to outclass others in a 1v1 game, which is unlike sports betting.