Creating a pretend game whose rules prove your point doesn't imply that your point is valid. It is akin to saying that 2^2 = 2 + 2, so therefore X^Y = X+Y.
This can work really well in a simple game we create solely for the purpose of proving it works well, but my point is that real-world "games," like international military conflict, are simply not as well-defined as everyone makes them out to be, and they are in fact a multiple series of games.
You cannot create a generally applicable theory by creating imaginary payouts and showing that game theory holds for these payouts.
Game theory cannot deal with situations where each party at any step in a game has multiple decisions, and subsequently optimal decisions will depend on the tactic chosen both in previous games, and the tactics expected to be chosen in future games. Game theorists have a hard enough time dealing with single games with multiple competitors. The more dimensions you add to your decision matrix, the less likely it becomes that a game theoretic approach would be optimal.
For instance, what if, in a series of games like the one you showed, I can lose out on any single game up to the Nth game, but push my adversary to become more and more irrational, until he is destroyed, and I get $1000 in every subsequent game, instead of $500, because I have no more competitors? Or I can get him to start behaving in such a way that I can get $750 and he keeps $250? If the game is actually a series of games, like in real life, and the rules and expected payouts are not well-defined, I may be able to do something like that.
No, it's more akin to if you said that XY is never equal to X+Y, and I pointed out that 22=2+2 is a counterexample. Your original statement, if I may remind you, was:
Game theory mathematics works in certain simplified games where your optimal strategy is to assume your opponent is rational. If the other party isn't rational, your optimal strategy works even better than if the other party is rational.
The underlined portion is false. There are plenty of "certain simplified games" where an opponent's irrationality changes the optimal strategy entirely, and plenty of strategies which are optimal versus a rational opponent which become suboptimal versus an irrational opponent.
I'm well aware of the fact that actual human interactions and geopolitical diplomacy would require a much more complex model.