I have 2 "full time" ETH mining rigs, one a triple R9 290, one a dual R9 290.

I have other rigs that bounce around, mostly between ETH and ZEC, depending on profitability.

 I mine through pools.

I have yet to see any anti-cheat system to detect computer assisted play. ... The only way this might work, would be to force speed chess.

This way the user will be penalized, while he inputs his opponents moves on a electronic device and waiting for the computer to make the

moves for him. People find ingenious solutions to cheat, so a smaller prize pot, would reduce the incentive to cheat. 

Is it logical to use GPU cards for mining? ASIC machines are special devices manufactured only for mining. These devices are returning after a while as scrap. But yet high-end GPU cards can still be used, even if they lose the mining feature. The GPU cards can be used on the computer to play games. It's easier to sell GPU cards as second hand.

What are your thoughts about this?

No anti-cheat system for online chess can check whether or not the player is using external devices to input the opponent's moves and receive suggestions.

It'd be fun, but nothing to be taken too seriously. With machine-assisted chess beating humans in all aspects, nobody smart enough to know this would put much money into such a thing unless playign with someone you trust beforehand.