Maybe we've redefined what patriarchy means, but going by the dictionary this article, and the associated viewpoint, is clearly reversing the cause and effect.

In context of broad society patriarchy is "control by men of a disproportionately large share of power". It is obvious that, given there are a small number of leadership roles, if one gender is more assertive, aggressive or violent (or indeed prone to risk taking - although the article does not mention that one) then that gender will end up with a disproportionate representation in the military and from there social leadership positions.

Patriarchy doesn't cause male behavior, male behavior causes patriarchy.

I'm throwing an assumption here that armies lead governments. Most countries need a few military victories early on to legitimise their control of territory.