The phrase “zero sum game”, taken as referring to the game theory thing, “zero sum games”, isn’t about wealth, but about utility (though sometimes utility could be modeled as just being wealth).
To say that something isn’t zero sum in this sense is a rather weak statement. If any combination of actions by people result in at least one person being worse off and no one else being better off, or in at least one person being better off and no one else being worse off, than some other combination of choices, that is sufficient to conclude that it isn’t zero sum. (This isn’t a necessary condition, only a sufficient one. But a Pareto difference (terminology?) implies a difference in the sum of utilities (assuming that there is a sensible way to add the utilities) without assuming a particular way to add utilities between persons, so I think it is easier to justify conceptually.)
That many things involving multiple people are not zero sum, in this sense, is obvious. (Punching a stranger in the face for no reason decreases the utility of the stranger without increasing one’s own. Well, for most people anyway?) It doesn’t imply that there are no limits to how good outcomes can be.
That a given thing is not zero sum is often something that would be sufficiently trivial as to not be worth saying, except that people talk about the thing as if it is zero sum.
If things were constrained to be on the Pareto frontier, then, while possibly still not zero sum, there would I think be less reason to point out that things aren’t zero sum even if they weren’t.
Pointing out that things aren’t zero sum is often, I think, effectively a call to take into account whether options would move closer to or further from the Pareto frontier, and not just pretend that things are always on the Pareto frontier and try to move along the Pareto frontier.
Now, if, within a certain context, the maximum distance it is possible to be from the Pareto frontier is negligible, then in those cases exclaiming “care more about the distance to the Pareto frontier!” wouldn’t seem to make much sense,
and perhaps even sometimes justice requires putting more emphasis on where on the frontier we are closest to than how close we are to it, even if it means non-negligible difference in closeness to the frontier.
But, generally speaking, Pareto improvements are good and important, and forbidding people from taking actions that result in global Pareto improvements (I don’t just mean “if you only consider these people, then among these people it is a Pareto improvement”, but rather things that are Pareto improvements when considering everyone’s interests) is usually bad.