I don't know how many people play four way chess, but do you have to checkmate an opponent's king or actually kill it to take over his army?
According to this site you can play Four way chess with the same rules that you play in a classical game (include the notion of checkmate) with the difference that all queens will start on white squares. All pieces have the same movements than on the regular chess, the first player to start is the white pieces play continues clockwise around the board each player moving one piece per turn.
Also according to this, you can play two variants of Four way chess:
- Regicide rules;
- Classical Rules.
Quoting the site:
Regicide means to kill the king, in Regicide Rules you must actually capture both enemy kings to win, rather than just checkmate them. When a players king is captured the rest of his pieces remain exactly where they are on the board and cannot move, except to capture another piece, or you may pass on any move after your king is captured. Your team must kill both the enemy kings to win. In Regicide Rules the king is a fighting piece too, so you dont have to get out of check and checkmate does not apply, and you dont have to announce check. You can even move into check. You can also castle out of check, through check, or into check.
and with the classical rules:
When one player is checkmated on his turn all his pieces are removed from the board and his two opponents armies combine into one army for movement purposes, being allowed one move from either color per move that the defeated players partner gets. This is how we used to play but now we usually play Regicide Rules.