"Shin" is definitely Shinmura or one of the higher ups (my guess is Shinmura because, come on).
This makes it pretty clear the organization, or at least a part of it, set up the circumstances they then preyed upon to start the game. (the third player is still a bit of a mystery. She's definitely important, but probably not in the same way Katsumata and Eyama are)
Eyama is definitely being set up for something, either a trap, or some sort of 'test' going along with whatever the real goal of the game is.
Glad this series got picked up again. They've got a pretty good mystery going for what was originally torture porn.