You're extrapolating from the payoff matrix for a two-person interaction to the equilibrium behavior of millions of people. You're also assuming rational actors, etc. You're making a mountain of assumptions here.
The equilibrium behavior of millions of people is just the aggregate of the behavior of individuals in small-scale interactions. A better objection would be that not all small-scale interactions can be modeled as two-person games.
Yes, I'm assuming "rational" actors, in the sense that they respond to incentives in a way that can be modeled by game theory. But that's not actually a very extravagant assumption. In particular, it does not entail that "rational" actors have to be conscious of the incentives they are responding to. I think many people who respond "rationally" to Prisoner's Dilemma-type incentives are not actually conscious of them; that's what I meant by my comment about tribal instincts. For example, saying that people punish defectors for emotional reasons rather than coldly calculated rational ones misses the point, because the emotions evolved in response to the same sorts of game theoretic incentives.
If you really object to the "rationality" assumption, then you need to come up with a better one. Attempts to do that (I'm thinking, for example, of the work of Kahneman and Tversky) often end up showing that the incentives involved are more complicated than we thought, not that we respond "irrationally".
The dynamics of a complex system cannot in any sense be described by simply aggregating the individual small-scale interactions.
In many cases it can, so this statement as it stands is much too strong. For example, a country's economy is a huge game of mutual cooperation whose dynamics can be perfectly well described by aggregating a huge number of two-person games (or perhaps "two-player" would be better since one player is often an organization, like a company or the government, rather than a single person)--or in some cases perhaps games with larger numbers of players, but still small-scale.
There may be cases where a system's dynamics can't be described this way; can you give a specific example?