To me it felt like the whole point of the novel was that Gurgeh was a piece in an even larger game and he didn't even realize it. So the idea that the people playing the "bigger" game couldn't compete in the smaller game seems silly, and I think they mention that they used Gurgeh instead of an AI to make it appear fair to the inhabitants of the planet.
The Culture is (in this story) pretty much only bound by their own constraints. They chose Gurgeh for the role, since he had enough skill and talent to actually be able to accomplish the Culture's (or the SC's, winkwink) objectives without having the whole thing being taken over by an AI.
The Culture worked very much like the PoG this thread is about: it minimised potential loss and considered the constraints it had to get the best possible outcome.
The Culture is mostly constrained by only ethical rules, which, admittedly, can get flexible, especially with regards to the SC. The practical restrictions, like it being easier to send one capable human than to conquer a small galaxy, are in my mind lesser in comparison.
As such, I think they got the most out of the operation, just by being confident in their assessment of a single human who played games good. And there's absolutely no reason to believe that the overminds that guide the Culture can't model human behaviour down to the smallest variable, especially considering how augmented humans are in the Culture.
I'm also 100% onboard the idea that all the drones could outplay Gurgeh in a blink in any game, intuition be damned.
The whole thing was about to blow up anyway, so they brought in the Player of Games, to do it in a style that would prevent any recovery. Gurgeh was not there to defeat the empire, he was there to defeat the whole idea of the game being "holy".
He was the Jesse Owen shipped to hitlers olympics.
You bring up a good point about shattering the view of the game though.
