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.