A theorem is a kind of statement that can be true or false. A strategy is a plan of action that can succeed or fail to achieve a goal. So you seem to be thinking of strategies in a nonstandard way. A strategy can be optimal and it may make predictions which will be either confirmed or disconfirmed, but strategies themselves are plans for achieving goals which are good or bad, not true or false. Anyway, this seems like just a semantic point unless it has some ramifications in your broader way of thinking.

Yes, some models or abstractions are useful in understanding rational behaviour. But the economists' models are fictions in that they refer to ideally rational individuals who don't exist. Only for an ideally rational person would life be literally a game. For the rest of us who are mostly irrational and who have incomplete information, these game theoretic models are akin to fables or to religious myths (albeit scientistic ones) that tell us how we ought to behave or that indirectly rationalize the creeping tyranny of computers in our environment.

For pragmatic purposes we can use whatever model we like to understand phenomena by simplifying matters. The problem is when we equivocate and forget we're being pragmatic and are tentatively resorting to models as tools. We mistake the map for the territory and blame people for not sufficiently emulating machines or we implicitly give a pass to bureaucratic automation and inhumanity, and to the sociopathy of business and political leaders.