I am not quite certain that I follow. Depending on tournament type R/P/S is (mostly) a game of chance, chess isn't. The only way I can see R/P/S applying is if they represent the players themselves, not the game. In other words, instead of having individual strength ratings that can be measured in isolation, player R's style of play might be naturally stronger against player S's style than that of player P, in which case we could only express the relative strengths of any pairing. This would allow a scenario where R is stronger than S is stronger than P is stronger than R.
However, given the pairing list of a tournament and the respective pairwise relative strengths, it is still possible to predict the outcome. As a very simple example, let's say that on the first round we have the pairs (rock_a, paper) and (rock_b, scissors). Winners of the first round (paper, rock_b) fight for gold, losers (rock_a, scissors) for bronze. Paper wins, followed by rock_a, rock_b takes bronze and leaves scissors last.
Applied to the problem at hands, one would suspect that there exists an algorithm not far removed from Google's PageRank that can identify all the possible playstyles and their relative strengths, in which case the simplest predictive model would contain the playstyle preference and proficiency of the players combined with style coupling constants (it is likely that a player can play several styles with varying degree of skill, and try to use the one that they believe to give them the best chances against what they know of their opponent). Just my hunch, I'm not really into this stuff.