The best description of The Economist's editorial position I've come across is the one mentioned in the linked article: classically liberal. The preceding comment about left-and-right clarifies nothing and is ironic given that the original article rejects the left-right characterization.
Also, you only need to read a few articles in the Economist before coming across the phrase 'this newspaper believes' which should eradicate any suspicions of objectivity, pseudo or otherwise.
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.
'Classical liberal' evokes thoughts of Adam Smith and David Ricardo, who have little in common with the staff of 'The Economist'. 'The Economist' is not alone in claiming this mantle, as Alan Wolfe has made similar statements (though his claim may be on shakier ground), but it is speculative and presumptive. The classical liberals did not envision many policies put forward by this magazine, and it is doubtful that Smith and Ricardo would have supported them.
Well, the simplest evidence of the statement you quoted is that they did not even agree with each other on many issues. A slightly less glib answer is that many of the policies which "The Economist" endorses, including fiscal, and monetary policy did not exist at the time, and/or were dismissed.[1][2][there are many more possible citations]
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.
There is no way in which The Economist is libertarian -- they believe in a very strong governmental banking system and frequently poo-poo countries for having too few taxes or too few government services. Also, reference the editorial opinion on government's role in health care.
Most of the old, classically liberal parties in Europe that formed the start of liberalism as a political movement fits politically from well left of Obama to pretty much where he is.
"Classically liberal" from a European viewpoint at least varies by country, but is generally considered as close to the political centre compared to e.g. libertarianism.
In many countries it would evoke social liberal ideas, in others it would evoke more conservative liberal ideas, but most will be found to the left of our conservative parties an to the right of our socialist parties (and often to the right of our social democratic parties). Overall, the "gravitational point" of "classically liberal" parties is probably centre-right.
So from a European point of view, it is a "useful descriptor" to the extent it places someone in a fairly narrow range in the political centre vs. for example "libertarian" which today tends to evoke firmly right wing populist or laissez faire politics (despite the existence of plenty left wing libertarian ideologies, such as left-communism, minarchism or libertarian marxism, but these are rarely described as such, and in Europe at least rarely self-identify as libertarian).
Also, you only need to read a few articles in the Economist before coming across the phrase 'this newspaper believes' which should eradicate any suspicions of objectivity, pseudo or otherwise.