How so? "Classically liberal" is a way of differentiating oneself from the modern definition of liberal and is basically a friendly way of saying "libertarian" without invoking images of Glen Beck.
Examples?
If you want to understand Smith and Ricardo's views in full, I suggest that you read "An Inquiry into the Nature and Causes of the Wealth of Nations" and "On the Principles of Political Economy and Taxation". There is simply no evidence in either of those books that the classical economists would support many policies outlined in "The Economist", other than free trade and free markets. The books describe more limited roles for government than you will find in the magazine.
It is equally obvious that the current classical, neoclassical, and Austrians have not and do not agree with "The Economist"'s advocacy for activist policies. Note: I view the Austrian school as the most evolved direct descendant of the classical school.
[1] Adam Smith-“The problem with fiat money is that it rewards the minority that can handle money, but fools the generation that has worked and saved money.” [2] http://socserv.mcmaster.ca/econ/ugcm/3ll3/ricardo/bullion
I agree with your definition of classical liberal, Economist doesn't subscribe to it.