Having watched a few BattleChess sessions now, the rules seem to be:

1. Each player has two or three chess sets.
2. The kings stand away from the battle (typical! ;-))
3. A player (white on the first move, winner on subsequent moves) brings forth four pieces.
4. The opposing player brings forth their four.
5. Each piece has a value and the combined value of your four players is what counts.
6. If your total beats theirs, their pieces are removed from the battlefield.
7. If it’s a tie, a coin is tossed to determine the winner.
8. The winner, naturally, is the player with pieces still standing.

The rules continually evolve as flaws in playability are detected. 🙂

I love this ingenuity and thought it worth sharing!