The policy of forcefully extending a nation's authority by territorial gain or by the establishment of economic and political dominance over other nations.https://en.wiktionary.org/wiki/imperialism
The second half of that is pretty spot on, and if I'm not mistaken some of the overseas bases did originate from the use of force.
Currently, the Pax Americana is based on the military preponderance beyond challenge by any combination of powers and projection of power throughout the world's commons—neutral sea, air and space. This projection is coordinated by the Unified Command Plan which divides the world on regional branches controlled by a single command. Integrated with it are global network of military alliances (the Rio Pact, NATO, ANZUS and bilateral alliances with Japan and several other states) coordinated by Washington in a hub-and-spokes system and world-wide network of several hundreds of military bases and installations. Former Security Advisor, Zbignew Brzezinski, drew an expressive summary of the military foundation of Pax Americana shortly after the unipolar moment:
In contrast [to the earlier empires], the scope and pervasiveness of American global power today are unique. Not only does the United States control all the world's oceans, its military legions are firmly perched on the western and eastern extremities of Eurasia... American vassals and tributaries, some yearning to be embraced by even more formal ties to Washington, dot the entire Eurasian continent... American global supremacy is...buttered by an elaborate system of alliances and coalitions that literally span the globe.
Besides the military foundation, there are significant non-military international institutions backed by American financing and diplomacy (like the United Nations and WTO). The United States invested heavily in programs such as the Marshall Plan and in the reconstruction of Japan, economically cementing defense ties that owed increasingly to the establishment of the Iron Curtain/Eastern Bloc and the widening of the Cold War.
Remember though that if not for US action, there would be no South Korea; there would just be a larger and more terrible North Korea, and millions more people would live in suffering and bondage.
Personally, I don't think the US should have intervened in Korea, for all the very good reasons that your founders cautioned against foreign intervention and entanglements.
But the intervention saved millions from enslavement. It was a net benefit to everyone in South Korea, then and now.
It wasn't the US alone - it was a UN-mission under the lead of the US, more than twice the South Korean soldiers fought than US soldiers, and don't forget all the other coalition forces who also fought: the British soldiers, the Turkish, the Australians etc.
If we go back even further, Korea as a whole was under Japanese rule. If the US negotiated with Japan instead of going all out, Korea wouldn't have to be split apart to begin with.
Also, if there was no South Korea, then who knows, maybe the "larger" North Korea would just be like China today; kind of terrible but not so terrible.
Without the US-backed South Korea, China would not be so interested in backing [North] Korea, and indeed would see them as a realistic threat rather than a client/buffer state.
