I think rounding that up to "drove the rise of civilizations" is a crude way to put that. For example, the simulation pits "agriculture plus military" against "agriculture". Then they found that including both food security concerns and physical security concerns more closely predicted known outcomes.
Had they put "agriculture plus military" against "military" and found that including both was better than just simulating physical security we would have gotten the title "Computer Simulations Suggest Food Drove the Rise of Civilizations".
I think the takeaway (besides how not to model and report on models) is that geostrategy is an important factor in the development of human and international relations and that broadly laymen are completely ignorant of it.
A layman equipped with some of this knowledge, for example, will be much more able to understand current events in the South China Sea, the infrastructure projects across Eurasia, the proxy war in Syria, the importance of the Crimea to Russia, the crisis in America over its policies toward Cuba, and much more.
Unfortunately the layman instead is fed a steady diet of "good versus evil" narratives, informing him instead about how he should feel about each case to emotionally and financially support his military.