Most of the games that you mentioned require skill as a precondition to do well especially chess which is not in itself gambling.
Regardless, however, gambling is by itself a stressful venture especially if your purpose primarily revolves in profit. Without that factor in mind, it could be considered as a form of mental sports like what you mentioned OP.
I may be wrong, but the only intellectual sports are chess, bridge, checkers, and Go. But not poker, betting, or blackjack. Of course, there are poker tournaments, but this is not an official sport. Moreover, sports betting is not an intellectual sport. There is a large element of chance in these gambling games, so it is incorrect to classify them as sports. Although they certainly develop intelligence to some extent.
I agree with you wholeheartedly.
Chess, checkers and other board games are skill-based games that require tremendous amount of knowledge in order to perform significantly better against your opponents. As opposed to blackjack and poker, which are still considered as "skill-based" games in the realm of gambling, those two (2) platforms are incompatible within the same comparison.