I think that's the wrong way to look at it. They do have skin in the game, in the sense that their readers wouldn't want to pay for a newspaper that is consistently wrong. And, even if they don't, it doesn't mean that it's not valuable
That's not quite what "skin in the game" means in this context.
The Economist does not need to be right, they only need their readers to believe they are right. That's not quite the same thing, and that small difference is what separates "skin in the game" from not having it.
They can get readers to believe they're right either by being right, or by being ambiguous enough to appear right in multiple futures. Professions where there's skin in the game don't have ambiguity and persuasiveness as an escape to the same degree.
You can confirm their biases, and need to do that to a certain extent to maintain readership. The quality of the media really depends in the demands of the customers consuming it.
Who cares if they're right about something? Are they putting money on the line? What is their P/L for being "right"?