It very much does. Boosting, a one of the best off the shelf ensemble classifier is derived from a game theoretic formulation. Besides that there is this huge body of literature about prediction under non-probabilistic sequence of test cases. This line of work is primarily held up by game theoretic arguments and that of online convex optimization.
Not a mention so far about game theory or Nash equilibrium.
It depends on what you're doing. I was literally just watching a video on Generative Adversarial Networks this morning, and game theory did come up there, at least in passing. If one sat down and started reading the papers on this subject and trying to implement / improve stuff in this area, I suspect game theory would be at least moderately important.
There is also the field of Competitive Learning where game theory has some application. See, for example: