On the other side of the link it says that the rules are essentially the same as standard Western chess. They say that you really can't improve on those rules. I tried though a while back with what was also a three player game, but on a hexagonal grid. It could also be played as a two player game.
It turns out that there are three main existing historical chess games, one Western, one Chinese - with a "river" down the middle that only certain pieces are able to cross, and Japanese - where when you capture an opponent's piece it becomes one of yours, which can quickly shift the balance of power, making for quicker games. All three games evolved from a Middle Eastern version with four players, where each player had only one rook, one bishop, and one knight, and the user had to roll a six-sided dice to determine which piece they would move.
A king came to power who was opposed to gambling and outlawed games of chance. This effectively destroyed the ancestral game which gave rise to the three branches that evolved over time.
My game combined elements of Western and Japanese, but rather than being able to use captured opponent pieces as your own you could take their "powers" and assign them to your own pieces. While I finished creating the game, I never really had the chance to play it with anyone other than a younger brother - and he wasn't especially interested. I didn't try that hard to get others to play it, though, as it seemed overly complicated to me.
As such, I am largely although not entirely inclined to agree with their view that you can't improve upon the traditional rules. Games, particularly complicated games like chess, evolve over time and over generations of players, who may tinker with them around the edges to reflect their own experiences. The tinkering is similar to mutation, and similar to the tinkering in the storytelling involved in the retelling of myths by different storytellers, or tinkering with natural languages by those who speak them.
The willingness of other participants (players, listeners and storytellers, and speakers) to accept a given change acts much like the pressure of natural selection. Complexity that is well-adapted to the constraints that are in place is the result. This isn't really something that is easily if at all replicated by a single mind employing a the top-down approach of an architect acting in accordance with some predetermined plan. It is necessarily an experimental process of discovering what works.