I can't speak for The Atlantic because I don't read it, but I wouldn't categorize The Economist as right-leaning. Its positions on various issues are too nuanced; I think it would be more accurate to decompose its views into economic and social issues. Then you end up with something that looks economically conservative and socially progressive. But even that sort of leaves out a lot of details that tend to get smoothed over in more mainstream political discourse.

Take a look at the Wikipedia page covering The Economist's editorial stance[1]. In particular, note their presidential endorsements and their respective positions on climate change, drug decriminalization/legalization and American military action in Afghanistan and Iraq.

To drill into a specific example, consider that they've historically endorsed Democratic presidential candidates more often than not; on the other hand they endorsed George W. Bush in 2000 because they agreed with his, "small government, pro-market philosophy".

While they haven't done it in recent memory, they have in the past abstained from making any specific endorsement for a presidential candidate. More recently they haven't shied away from criticizing both candidates.[2]

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1. https://en.wikipedia.org/wiki/The_Economist_editorial_stance

2. Here's a fun one: in 2004 The Economist very weakly (and sardonically) endorsed Kerry by saying, "The incompetent George W. Bush or the incoherent John Kerry." In contrast they gave two ringing endorsements for Obama.