This variant, created by Bruce Zimov in 1972, introduces an interesting goal - to checkmate a knight instead of a king. It means that each player has one knight (at the standard king position) and two kings (at the standard knight positions) - see the next picture:
Regarding this modification, some classic Chess rules are changed as well:
A castling move can be done with the knight and a rook, following standard castling rules (neither knight nor rook may move prior to castling, no other piece may block the castling move path, the knight must not be attacked by an opponent's piece, no square between the knight and the rook may be attacked by an opponent's piece).
Kings can be captured like any other pieces.
Since the knight plays the king role, it cannot be exposed to a check and it cannot move to a square which is under direct attack of an opponent's piece.
A pawn can promote to a king and cannot promote to a knight.