From a technical standpoint, what's happening is that New York Times is running arbitrary code that it doesn't know anything about on the browsers of people that visit their site. And they are claiming that they are not responsible for what it does, despite the fact it's delivered through New York Times.
Does any company in the world that serves ads from Google not do this or state this?
How would you technically host ads on your site without "running arbitrary code"? How would you add an analytics solution without doing that?
And also, focusing on this defeats the actual purpose of this article. I assume it means you agree with it's message and are just nitpicking? (Or don't and are deflecting.)
And no this is not something they have to do. The idea that they cannot control what their vendors do is completely absurd - they have contracts with these vendors so they can state exactly what vendors are allowed to do under these contracts in the privacy policy. The only excuse here is that they are either too embarrassed to put what's in these contracts and/or they have no idea what's in those contracts. What NYT is doing is more or less equivalent to selling their users' data, which Google does not do.