I would agree with @Wildan a player can use other computer to cheat so it doesn't make sense on having a bet on a Chess game but that would be great if anyone can stop people from cheating (Which is not) for me adding a bet on Chess game could spice up or make the game more intense.
It is possible to have a this kind of game if the player could have a live webcam to them (to see if they are using other computer) and a screen share of their computer just like what they are doing in online chess tournament but that was too much right? Setting up cameras and sharing your screen to others.
In fact, cheating among strong and even average players is practically not used. It makes no sense (in serious games and tournaments) because computer analysis quickly reveals the use of third-party programs. Strange as it may seem, the player's chess behavior is very easy to predict, and if he "suddenly" starts to play better than his level, this immediately attracts attention. In addition, if a player plays games as first lines of chess engines, then he automatically receives a ban on almost all chess sites.