Game theory is totally legitimate. The problem comes when non-mathematicians try to wield it. They have a superficial understanding of the underlying math, they certainly haven't read the criticisms of the theory. They don't understand why it is useful, why it was developed, or what it's limitations are.

GT is a mathematical abstraction that relies on the assumption of rational actors. It was originally applied to the nuclear standoff between the USA and the USSR. The stakes in nuclear war are so incredibly high that each side was forced to think very rationally about its behavior. In most other real world situations the stakes aren't nearly that high, and people are not entirely rational. Game theory therefore does not apply.

The problem of people misusing science certainly isn't limited to game theory. For example, there are vast number of articles and books that make bold claims about human nature based on a flimsy understanding of neuroscience and/or evolutionary psychology. Most legitimate scientists are actually extremely cautious about making bold claims about anything. The whole basis of science is that there is very little that you can actually know for sure.