Well, is is certainly possible to question whether the American Revolutionary War can really be called a revolution. There's an old classic, by Crane Brinton, called Anatomy of a Revolution. Brinton , looking at the English, French, Russian and American examples, found some common aspects: an early reforming phase; an incompetent, inflexible government that can't be reformed; a radical violent de-construction of that government, with power devolving down armed bands down at the local level, then a reaction against the radical phase, with great authority given to a military figure. Unfortunately, Brinton only looked at a few revolutions . But still, only looking at a few of these events, it was hard for him to fit the American revolution into his scheme. There really was not a radical phase, where power devolved down to armed bands at a local level. The local elites who governed the Colonies before the war continued to govern the states afterwards. There were some incidents, like Shay's Rebellion, that worried those elites, made them fear armed mobs might possibly rise up to knock down the hierarchy- but that did not happen.

This has had a variety of political interpretations- as you can expect. Some people on the left would like to see this as a failure, that the Revolution was orchestrated by wealthy elites who only wished to aggrandize their own power, and that the rhetoric about Rights of Man was never extended to freeing slaves or coming to terms with the Native nations. They have a point. Washington demanded all escaped slaves be returned, after the Battle of Yorktown- many had sheltered with the British Army. Many Colonists saw the war as freeing them from the Proclamation of 1763, that kept them from moving into Indian lands west of the Allegheny Mountains. But the war was popular- all classes of people were in the Continental Army, all sorts of them hated the Stamp Act and the Intolerable Act and the military crackdown on Massachusetts, and felt Britain was acting like a tyrant.

People on the right prefer to see the War as an example of American exceptionalism, as you say. That we just did it correctly, were moderates. Certainly, moderation was there. The Loyalists who did not leave were not shot after the War concluded. During the War they had been treated very roughly at times ( especially in North Carolina) but there was no bloodbath of retribution with firing squads afterwards, and they were even allowed to regain their property - if it hadn't been burnt- and participate in the new country. Nor did the members of Shay's Rebellion actually suffer greatly. The military response to them was pretty mild, they surrendered quickly, and most were pardoned.

But perhaps luck was more important than ideology, perhaps moderation was possible because the fight never became desperate. The Colonies had much help from the France and Spain, both money and military assistance ( especially the French at Yorktown) . And the British effort to regain control was pretty half-hearted. The North Atlantic colonies were sparsely-populated, mostly by farmers, and were economically much less important than Jamaica and the Caribbean. The 18th c. was a time of almost constant war for Britain, and it was easy for voices in the British government to complain that fighting for control of the North Atlantic colonies was just not worth the trouble. So, another good reason why it did not become radical is because the British were willing to stop fighting, allowing the existing colonial governments to simply assume complete control.