I'm sure you're right that game theory predicts that societies would develop rules to govern their behaviour, to avoid the worst foreseeable outcomes. The question is whether morality is just another set of prudent social conventions along with the need to coordinate car drivers and to restrict them to one side of the road.
We plan our societies to that extent, calculating the most efficient way of organizing our interactions. We write out the laws with the greater rigor to make them airtight.
But all of that seems to presuppose the difference between right and wrong. Morality is about that fundamental distinction, which depends on our ability not just to imagine possibilities, but to condemn a state of affairs in relation to an ideal. I don't see ideals arising just from bureaucratic calculations. Bureaucrats presuppose the ideal and practice instrumental rationality.
I wonder whether it's telling that you automatically discount species suicide as immoral. That suggests that game theory isn't just predicting the existence of rules, after all, but has a hand in constraining the content of those rules (at least in the societies that take evolutionary psychology seriously).
You say morality is at least a way of enabling our survival. But as a matter of fact there are moral systems that condemn human nature as "fallen" or as inherently corrupt and diabolical. Aren't we capable of imagining self-destructive moral systems which therefore fall outside the scope of evolutionary morality and thus game theory?
Or would you want to say that game theory can explain failure only after a society labels some behaviour as bad?
In that case, game theory would be comparable to the psychiatric definition of mental illness as social dysfunction. The psychiatrist wants to be scientific and therefore value-neutral, so she waits for society's values to arise, which enables the psychiatrist to get around the philosophical problem by presupposing the goodness of social functions.
Individuals can be dysfunctional relative to social norms, whereas society can't be dysfunctional relative to individual human potential. That's the presupposition which led to the psychiatric condemnation of women and homosexuals, for example, and which puts Western psychiatry in the pocket of consumerism.