I think we have to be really careful to specify which "patriarchal" we mean--whether it's colloquial, social science, or something else. One main focus of male-power-dominated societies has sometimes been to take care of women and children first and put themselves last. Being the breadwinner means you obtain the bread, not that you eat it all or even the best part; it could also mean that you give it to the people you love and keep for yourself the bare minimum that you need to go win more bread.

However, when you are in power, there isn't really anything forcing you to put yourself last, so it's hard for the reality to line up with the rhetoric in that regard.

In any case, it's perfectly fine to define "patriarchy" as "women take care of men and put themselves last" and also "everything is zero-sum". But if you say it and other people don't interpret it that way, it's mostly your fault for not being clear, because the dictionary definitions, for instance, don't include either of those things.