Any game could incorporate wagers into its rounds. You could bet on plays in a football game. You could bet on matches in Chess. However, the competitive foundation isn't predicated on these wagers. This allows for more dimensions of skill variation because game participants can take risks that won't kill them.

In Poker, especially in tournaments but over time in cash games as well, there will necessarily be more losers than winners. That's a fine outcome for a competitive environment, and a terrible outcome for an economic one. And because placement is based on willingness to play at certain stakes instead of skill rating, the entire system is designed to mismatch the skill of the participants over the long term.

Betting on probabilities is an entertaining way to adjust levels of confidence to reality. I just don't really like the idea of promoting gambling to children.