Since I presume you're a techie, it's funny that you overlook the main reason for Luther's success, which was technological—the invention of the mass-printed pamphlet.
Mass communication was also a factor, but probably not one that Luther would have grasped until he was already committed. And he wouldn't have printed any pamphlets if the local authorities executed him immediately.
As for game theory being a toy model, every model of human behaviour is a toy model. I'm not sure if game theory is a particularly bad one.
I think the conclusion from that argument, which I'm honest-to-god surprised to see 'idlewords making, is that if not Luther, then it would be someone else a month or a year later, because a) the forces that shaped Luther were present in other places, and b) it's the printing press that made the Reformation stick (there were earlier attempts, which failed).
There is one shining result in mechanism design, a subfield of game theory, called the revelation principle. It says, simply, that if one doesn't like how the game is played, one may design the game that they want folks to play, and offer incentives accordingly, and people will play the game according to the incentives.
While this may sound like academic bullshit, it is the closest thing you'll find to a solid philosophical foundation for why proof-of-work or proof-of-stake systems should be expected to work in practice as well as they do.
Game theory is more advanced than the prisioner's dillema, but unfortunately that's what's discussed in 99.99% of examples. And yes, it is a toy example.
https://en.wikipedia.org/wiki/Propaganda_during_the_Reformat...
I would also urge you to resist the lure of game theory in analyzing human behavior. It's a toy model that gives toy insights.