The rules of Chess apply, with one modification: Empty spaces that would, under the normal Chess rules, be threatened by an enemy piece, do not exist for your pieces, except for your king. This means Pawns can run across the board in double-quick time. The Pawn pictured below can step over the nonexistent intervening space to capture the threatening enemy Queen.
 
The implementation was done based on the limited information from the Chess Variant Pages.