What would stop the Atlantic from "getting sued into oblivion" is that the person that the article was about (Nixon) was dead when it was written, and the dead can't be defamed.
It doesn’t prevent them from suing,
It does, within its scope, prevent the US or (because the same rule is incorporated against the states under the 14th) any state government from giving them a legal basis for winning a suit, though, which the target of a suit is free to point out to the court to get the case dismissed. This is why the scope if defamation is much narrower in the US then in the British law it inherited.
And, in some US jurisdictions, the target mught also be able to recover damages from the filer of the original suit under anti-SLAPP. laws.
The bar is especially high for defamation of public figures like Nixon. For something to be defamation against a public figure, it not only has to be provably false; it has to be intentionally and maliciously false. They would have to prove that the author intentionally was spreading false information to hurt the subject. That is so difficult to do that defamation suits regarding public figures are almost never successful.
It doesn’t matter if “well it’s not technically illegal because it’s not the government”, people don’t like censorship either way.
If your only defense of [corp/group] is that “well technically their suppression isn’t against the law” you’re probably on the wrong side.
How would lawsuits work without the government being involved?