It is a formal calculus, not an empirical theory.
The term "theory" is ambiguous. Sometimes it refers to a hypothesis as to the forces that govern the course of events--this how the term is usually used. Relativity Theory is a theory in the sense, as are evolutionary theory, quantum theory, and psychoanalytic theory.
But sometimes the term "theory" refers to formal calculi. A formal calculus is simply a class of symbols coupled with a grammar that is defined for this symbols, a grammar being a set of rules saying how those symbols can be combined into larger symbols.
A formal calculus is "uninterpreted" when no meanings are assigned to the symbols in question, and otherwise "interpreted."
Game Theory is an interpreted formal calculus, since the symbols in question have been assigned meanings.
When formal calculi are developed, there is usually an interpretation in mind; and sometimes it is believed that, when coupled with that interpretation, that formal calculus tracks some kind of empirical reality. In other words, when a "theory", in the strictly mathematical sense, is developed, it is sometimes because it is hoped that it will also turn out to be a "theory" in the empirical-scientific sense.
This was certainly the case with Game Theory, which, so it was hoped, would track actual economic conduct.
But Game Theory proved rather useless from that viewpoint. Yes--people generally act in their self-interest. But until we know what a given person believes his own "payoff matrix" to be, we can't use the technical apparatus of Game Theory to predict what person will do; but if we do have that information, we don't need Game Theory.
In fact, Game Theory is nothing more than Adam Smith's Rational Actor Model but with a lot of confusing mathematical sophistries piled on it, which make it hard to apply and which, in any case, have not yielded any predictions that Smith's model did not yield.
When people talk about the "applications" of Game Theory, they are usually talking about applications to 'auction theory" or some other totally non-predictive branch of economic theory.