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Without bothering to go to the website, it sounds a little bit like 'New Eleusis' ported over to the chessboard. 'New Eleusis' or however you spell it was a cardgame popularized in the 1960s, and popularized again in the 1970s by Martin Gardner in his Scientific American column, Mathematical Games. It involved one person, the Rulemaker, and all the others were players or proponents of mathematical rules that would explain which cards could be played on top of, or subsequent to, a starting card. You see, the deck could be shuffled or unshuffled, it didn't matter, as it depended on what the rulemaker approved. Let's just assume they were shuffled. Anyway, the game was started with all the players getting a handful of cards face down that only they could look at, or manage. Nobody could look at the other person's hand. The only cards in plain sight, were those of the tableau, beginning with the first card of the remainder of the deck turned up. You might consider it a form of competitive solitaire, in a way. But the important thing is, the Rulemaker would either say 'yea' or 'nay' on the play of a card. Everything is predicated on the Rulemaker secretly recording a rule - e.g., play a red card after a black card, but anything can be played after a red card - and that was it, that was how the game was played. The object of the game was not just getting rid of your cards (though that was not enough to win, as you just got more cards after that), rather, making a declaration as to what the rule was - and being able to prove it, by looking at the rule that was written down.

With Stanley Random Chess, there appear to be self-appointed prophets having divine knowledge of what the secrets to the game are. How unappealing. For the game to have some kind of real value to it, the rules behind it must be recorded somewhere, and disclosed within a fair amount of time, so nobody has reason to call anybody else a cheat, or the Rulemaker an idiot. Although 'New Eleusis' has value as a mathematical game, I don't see the same thing with a chess game of this kind.

BTW, the difference between 'Eleusis' and 'New Eleusis' was the creation of an extra role - somebody would be a self-declared prophet interceding between the cardplayers and the rulemaker, and so long as his prophecies were correct, he garnered points for himself, and remained prophet.