Cortes continues the tradition of de Maistre by endorsing the situational dictatorship - "just" usurpation of the throne from incompetent traditionalists in order to restrain the onslaught of liberalism and communism. Schmitt actually regards Cortes as the more radical of the two, contending that Cortes's thought portends the rise of atheistic/agnostic reaction in the form of Maurras and others.
But I agree to a certain extent. Maistre was tilting toward a new type of conservatism and reaction that eschewed the dusty and feeble attempts of the old order to preserve what was surely a decadent and stagnant culture. Maistre's vitality was a stark contrast to the sickly and infirm ancien regime and probably stemmed from the fact that he was not of the ancien regime but rather of a recently ennobled middle class family.
Nobody is claiming he was a liberal. If anything the article is negative toward Thomists and tradcats, not de Maistre.
Well, I am actually the author. That's my blog, to tell the truth.