Not really, you can write a just-so game theoretic story for everything, that doesn't mean it's true.

There were too many instances of countries not only resisting Mongols against really bad odds, but also of more ridiculous actions like killing Mongol envoys for no apparent reason, even when Mongols weren't trying to invade. I've never seen anyone using game theory to even make testable retrodictions for historical actions with any success.