How does Game/PUA theory cause men to have increased success in having casual sex with women (assuming that it indeed does work)?
Possibly because it acts like a placebo does: it's the belief that Game works that is enough to imbibe the neophyte individual with enough confidence in them to believe that he will succeed with his goal of having sex with a woman. So in this manner, it's not the theory, the practice or anything else to do with the practice of Game that causes him to succeed, it's the 'belief' of success that is associated with Game/PUA that will cause him to succeed.
It's like someone giving you a sugar pill to cure your headache and telling you that it is made using the latest scientific know-how and expertise. You'll believe it because it has the appearance of credibility, and then your headache will magically go away, although you could have cured the headache yourself by simple belief.
It's also like a man with letters before and after his name, wearing a white lab coat, a pair of glasses, and a beard telling you that Global Warming is real. It's the illusion, the belief that the man in the white lab coat inspires within you that causes you to believe that it's true. Global Warming isn't true, natural solar cycle and localised environmental modification (pollution, deforestation etc) are true, and it's these that are causing the continual change in regional and global climate. It's the appearance of credibility that causes you to believe the man, rather than question him and determine the truth for yourself.
There's no doubt that some elements (either theory or practice) of Game are actually objectively true, Hypergamy for instance, but that doesn't take away from the fact that it is just the placebo effect of the whole PUA/Game culture that causes potential clients/adherents to have an increase in success. And so remember that it's not Game that you need in order to succeed with women, it's just that you need belief. And belief is something that you get from yourself, not from anyone else, be they in a scientific lab coat, effete-dandy coat, or business suit. Get belief from within yourself and determine what's true for yourself.