Good post, always enjoy Claremont articles.
He almost gets it, but he muddies the water still by confusing "conservatism" as its usually used, with American "conservatism" which is, at its heart, classic liberalism. American "conservatism" has as its twin fathers John Locke, Mister Classic Liberal himself, and Edmund Burke, the Father of Conservatism, who was a Whig - that is - a classic liberal.
Because for "conservative" to have any particular meaning, we have to define what it is that we seek to conserve. Most of us would say that we are Constitutionalists, referring back to that most classic-liberal of documents. What Burke sought to lift up were those traditions and rule of law that tended to limit the authority of government, that tended to preserve the liberty of individuals. It was not "tradition" per se, but a very specific subset of tradition.
The royalist "conservatism" of other times and other climes never had anything to do with American conservatism, because it tipped its hat to other traditions.
But our most sophisticated European cousins, and our sophisticated friends in the Democratic Party never get it, and so waste most of their time arguing with their own shadows.
What we now refer to as "liberals" are not liberal at all. They would best be referred to with other words; our Uncle Fred who we like would probably best be called a populist; the nutball professor we don't like is a socialist when he isn't a full blown marxist or fascist or both (the article does note that between fascism and marxism there isn't much difference; fascism is communists trying to run businesses).
The better way to explain the difference, is to understand that the great historical argument is between Locke and Burke on the one hand, who believed in limited government, versus Rousseau, who was the father of activist government. In most of the world, Rousseau won; Locke and Burke won only in the US, and the war isn't over yet, Rousseau's minions never give up their faith in the Will of the People as encarnated in centralized governments everywhere.