Two (of many) extant points appear worth a quick comment - military advantage is not the only descriptor of a hegemon, nor was it for the Romans, whose political culture was at least as influential as its legions. Hegemony, therefore, must have military advantage among other influences in order to be complete.
In all three models, however, the Macedonian, Roman, and Mongol, the military was far more influential within its host society than the U.S. military is within its. There is peril here in analogy - the older Greek culture enjoyed a considerable cultural hegemony over both the Macedonians and the Romans, and the older Arab culture a similar cultural hegemony over the invading Mongols by way of religion (and the earlier Seljuk and the later Ottomsn Turks). Who then shall be declared master? Is there a similar European cultural hegemony over the United States, and what are the merits of the persistent complaints that it's working the other direction?
Clearly these are matters outside the scope of this paper. But any general application of power geopolitics cannot be restricted to military advantage if it is to begin to explain what appears to me to be an unprecedented world alignment. I suspect, though, that the "adapt or die" message of the paper might be applied very much beyond military advantage in this consideration.
Just some quick thoughts. More later after a thorough read.
In those occupations, we projected power through NATO, which is more closely modeled on those many Roman Legions that rarely ever saw Rome were often foreign-speaking troops.
Roman control was cemented by Roman currency and Roman weights and measures. That forced Roman language and political culture which still endures.
Not sure I agree on the Macedonians, they were a rough, warlike, and crude culture within Greece and were rarely accepted into polite company.
Good points never-the-less, and this paper needs much study to get its points.