I recently came across a diagram of that chess board and a very brief description of the rules. The board is divided into three main levels each containing 16 (4 by 4) squares. In addition, each player has two attack planes of 4 (2 by 2) squares that can hang above or below each of the three levels. Moving an attack plane counts as a move and changes the three dimensional geometry of the board.

The rules are bit ambiguous but they could be worked out. I'm not much of a chess player, but it might be fun to make a HyperCard version of this game. Is anyone else interested?