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I'm reading Tom Slee's book No One Makes You Shop at Wal-Mart, and it applies game theory to some dressed-up toy examples (prisoner's dilemma, coordination games, etc.) to demonstrate why agents making individual decisions to maximize their utility (representing consumers using the power of individual choices) can fail to maximize their total utility (representing the failure of individual consumer choice to secure optimal outcomes for consumers).
[Edit: I should note that Slee's book isn't very technical, so maybe it's more evidence against needing the full-blown mathematical machinery of game theory? I'm about 100 pages in and it hasn't gotten much more hardcore than tabulating the results of games in a payoff matrix and an informal explanation of Nash equilibrium.]
The machinery is still there, even if you can't see it.
Good point. What I mean is that lots of readers could still get some mileage out of game theory without having to know the rigorous mathematics underlying it (although as you say the mathematics is still there even if someone doesn't know it's there). For example, I don't need to know how to use a fixed point theorem to prove the existence of Nash equilibria for all finite games to be aware of why the prisoner's dilemma is a sticky situation.