As I understand it, game theory is a set of mathematical tools for modelling social conflicts. It was originally egoistic, but it branched out for left-leaning models. I try to cover both types in the article, because it's possible game theorists try to obscure the dubious egoistic presuppositions of their approach.
In any case, game theory operates at a meta-ethical level. It's about the need to strategize to solve some practical problem. Consequentialism, deontology, and virtue theory would be the tactics used in the negotiations needed to overcome the problem.
But I suspect that what the game theoretic approach to morality tends to imply is an elimination of moral questions, a reduction of them to questions of instrumental rationality, assuming the overall goals in life can be presupposed or "externalized" by these models. The idea is to colonize this philosophical territory, planting the flags of capitalism and economics in what was formerly an autonomous discipline.
Moral questions are supposed to be solved collectively by the same kind of ground-up bargaining that tells us how to price our goods. In short, the free exchange of ideas and the invisible hand solve all of these problems.
Instead, the moral questions are typically dodged or their answers are presupposed by the unreflective majorities and by the technocrats, which is why philosophy became an independent discipline in the first place. Those three philosophical schools represent three answers to the hard question of morality (What should we do in life?): we can strive to maximize happiness, to be rational, or to moderate our character to fulfill our natural purpose.
In so far as game theory says we arrive at our morality after some negotiation, it doesn't really address morality itself. It's the same with social contract theory, since that framework was compatible with monarchy (Hobbes) and with liberalism (Locke). The main point of this theory is that society reflects some kind of idealized pact we make to avoid the alternative that's worse than any society, namely life in the wild. Again, it's stating the obvious, but it's dressed up as a "theory."