"Hegemony" as a term is used every day and doesn't at all neccessarily have to do with economics. Hegemonic powers through history include, the roman empire, british empire, and until recently, we had dual hegemonic powers in the form of the US and the Soviet Union.

Hegemony simply means dominance. We are the dominant power in the world today. As a result, we are seeking to bring peace through our hegemonic status- rogue nation states are reigned in to protect our national security and further world stability. Its not at all unlike the Cold War when countries such as Turkey, Iran, etc, falling to the communists were seen as a direct threats to our security despite their geography, capablities, etc, which leaned towards them not being terribly threatening.