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).
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.