You can send the replay of client actions taken, including the random seed to be sure the board and subsequent random results are accurate. A bejeweled game probably represents a few KB of data in this format. Here's the seed, a list of which two gems were switched, and when special abilities were activated. Done.

Chess has a standard notation, and there's even tools to detect when human players are cheating by having chess engines play their moves by replaying parts of the game to those engines and checking for too many move similarities.