How do I reconcile this with "entropy invariably increases" which is a contradiction to your hypothesis that "nature tends to favor zero-sum games"?

How do I reconcile "for every chemical and nuclear reaction, when something is gained, something else is lost" with catalysts increasing rate but not being consumed themselves?

In fact you can show there are an uncountably infinite number of broken symmetries in nature, so it is mathematically possible to concoct a parallel number of cases where nature does not have some "zero sum game" by Noether's Theorem.

Your statement is just cherry picking a few and then (uncountably infinitely) overgeneralizing.