If knights are allowed to move (or are captured, clearing the way), castling may become possible, but only on the kingside.
Because the two kings must occupy squares of different colours, they are allowed to be located next to each other.
Smullyan's example asks: What color is pawn g3 – white or black?
In Bichromatic chess, the opposite restrictions apply.
Hence pawns cannot capture (or advance two squares) and bishops cannot move.