I found the same link, as provided by Analoguesat, when searching, and there are 3 different options, for the game.
Copied from Boardgamegeek:
Rules of the game:
--- 1 ---
Queen, Tower, Bishop, Knight
The players take the four pieces of their color and place them in turn on the board, trying to place them in a strategic way, knowing their value and their movement, in order to avoid losing them too quickly. As soon as the 8 pieces are placed, the players can move one their pieces in order to capture those of the adversary as fast as possible.
Goal of the game: To keep the most pieces in play. The game is over if no captures are made in 5 consecutive rounds. The winner is the one whose pieces has the highest sum of values.
--- 2 ---
Tower, Bishop, Knight, "Queen-Pawn"
In this alternative the Queen metamorphoses herself in simple Pawn. This piece can advance or to move back of only one box and it captures only in diagonal. As in the first rule of the game, the playes alternate in placing their pieces before moving them.
Goal of the Game: To take all the pieces of its adversary. The part is stopped at the end of 5 consecutive turns without captures. The winner is the one whose pieces has the highest sum of values.
--- 3 ---
Tower, Bishop, Knight, "Queen-King"
In this alternative, the queen moves as a King. The objective of this game is to protect the King so that it is not put in position "checkmate". The Queen-King is in "check" when she is threatened to be taken by an opposing piece. The attacker must then announce "check". If the attacked player cannot prevent his Queen-King from being taken in the following turn, it is "checkmate". It can happen that a player has it's pieces blocked, and that he cannot move his Queen-King Without putting itself in "check". In this case, it is "stalemate".
Goal of the Game: To put the opponent in Check-Mate
--- Value of the pieces ---
Queen : 5
Tower : 4
Knight: 3
Bishop: 2
Pawn : 1
-- Movement of the pieces ---
All the pieces move exactly like in ordinary chess, with one exeption: The queen-pawn. In Chess-Quito the pawn can move one square forward AND backward, and capture in all four diagonal adjacent squares.
The pieces don't seem to have a starting position, each player places them, in turn, anywhere on the board.
Thus if you start, and select your Bishop, you place it in the most advantageous position, or where you think it's best, your opponent then seems to be allowed to pick any of his pieces, and place it where he thinks is best.
Only after all the pieces are in play can you actually move them, like chess pieces, except for game 2, and the queen becoming a pawn, for moving, but a bishop, when taking.