In this variant, both players have to move their kings closer to each other every 5th move, until they are as close as they can legally be. At no point are they allowed to move their kings further away than the closest they have been at any point during the game. Distance is calculated as king moves, so castling is still acceptable, as diagonal moves still allow a king to reach the other king in the same number of moves as orthogonal moves, however, if a player's king is not able to meet the requirement of moving one square closer to the other king (measured in king moves) when a mandatory king move comes around (up until the kings cannot legally move any closer to each other), that player automatically loses. Once the kings are as close as they can legally be, the game continues normally until checkmate, except that the kings are locked at the same distance from each other, unable to move further away.
In this variant, both players have to move their kings closer to each other every 5th move, until they are as close as they can legally be. At no point are they allowed to move their kings further away than the closest they have been at any point during the game. Distance is calculated as king moves, so castling is still acceptable, as diagonal moves still allow a king to reach the other king in the same number of moves as orthogonal moves, however, if a player's king is not able to meet the requirement of moving one square closer to the other king (measured in king moves) when a mandatory king move comes around (up until the kings cannot legally move any closer to each other), that player automatically loses. Once the kings are as close as they can legally be, the game continues normally until checkmate, except that the kings are locked at the same distance from each other, unable to move further away.