Historical Origin of the Terms
The usage in Western politics of "right" and "left" to refer to political affiliation stems at least from the French National Assembly in 1789, during the French Revolution. There, the Second Estate, or nobility, sat to the right of the chamber, and the Third Estate, or common people (at the time the radicals) to the left. Thus, "right" generally meant conservative, upholding the existing social or political order, and "left" meant radical, attempting to change or overthrow the existing order. The usage may actually be earlier, from the pre-Revolutionary Estates-General, where right and left referred to supporters and opponents of the monarchy.
That is a correct statement. If you read Chapter 7, The Lies Of Socialism, I make a similar argument, in my long list of examples of the Leftist position of the National Socialists. By your definition, above, the Nazis were clearly and unambiguously on the Left and the Founding Fathers were on the Right.
The Foundig Fathers were basically defending their existing orders, built up by the various settler societies literally from the ground up, from a new level of British interference, following the French & Indian Wars--our part of the World War known as the Seven Years War. They were hardly trying to undermine the social structure of their own creation.
Chapter 12, Political Spectrum just illustrates the verbal argument from Chapter 7, and basically illustrates your example from the French Assembly, but adopted to a more general analysis of other nations.