There is a way to circumnavigate around the cheating issue: Let 'em!
If Crypto-chess-coins is going to dole out coins based on some exponential growth system, then along with each game getting harder and harder to play, assuming one is playing against a computer which Ccc controls, Ccc will also control the clock as to how long it'll take before it makes its next move against each and every "miner". Thus, it doesn't matter how long it'll take for a miner to make s/he's move.
The onus will then be on the miners to obtain the best chess program available to garner more wins over time. At some point, when such is more difficult to obtain, more powerful chess programs will need to be created. Imagine, in the future ordering said programs/systems/rigs from Rook Labs or Bishop Studios or Knight Mills or Queens with Clubs.
Who knows! At the end of the day some über-chess program my be devised that wouldn't have been created earlier due to the advent of Crypto-chess-coins.
Now, one's able to envision Solitaire Coin, Backgammon Coin, or even Puzzle Coin, all pegged against a computer opponent with a dual difficulty component incorporated, adjusted depending on the payout schedule.
During the penning of the last paragraph, I envisioned something pertaining to Puzzle Coin, but I see that
http://puzzlecoin.com/ is already taken, but from the looks of the site, it could easily be re-branded.
Picture sometime like below that has to be solved via moving the pieces into place, then rewarded once completed. See the beauty of the example? Advertiser's logos (with generated links once solved, then also emailed) are the puzzles.

I agree!
It now becomes a contest of who can either write the best chess program and/or throw computing power at it.
One way is to use the chess scoring system, and the nodes accept the block created by the highest scoring address at the time.
Nodes can verify all games and scores quickly from the genesis game of course.
Any newcomer who is good can quickly rise to the top due to how the chess scoring works, but as they get near the top they need to beat the best continually to get the top score.
There are a lot of security things to be thought of e.g. shill players who lose on purpose to boost another players score.
There is no need to have difficulty adjustment because it is always as difficult as whoever is playing at the time. And there is an financial incentive for miners as with bitcoin so plenty of "hash power". Or should I say "horse power".
I'm a coder and be interested in helping develop something like this, a prototype at least.
Edit:
Man this is really interesting -E.g. I just thought would you build a program to try and win all the time or not? Winning all the time would take more resources, so you play less games. Or do you play more games and win 90% of the time. Which would give you a higher score? So much scope for miners to think rather than just throw money at asics like you do with bitcoin. Infact asics would be a disadvantage because you can't change the algorithm when a better one comes out next week.