More critically, while fair use decisions are famously a judgement call, I think OpenAI will lose this based on the "effect of the fair use on the potential market" of the original content test. From https://fairuse.stanford.edu/overview/fair-use/four-factors/ :
> Another important fair use factor is whether your use deprives the copyright owner of income or undermines a new or potential market for the copyrighted work. Depriving a copyright owner of income is very likely to trigger a lawsuit. This is true even if you are not competing directly with the original work.
> For example, in one case an artist used a copyrighted photograph without permission as the basis for wood sculptures, copying all elements of the photo. The artist earned several hundred thousand dollars selling the sculptures. When the photographer sued, the artist claimed his sculptures were a fair use because the photographer would never have considered making sculptures. The court disagreed, stating that it did not matter whether the photographer had considered making sculptures; what mattered was that a potential market for sculptures of the photograph existed. (Rogers v. Koons, 960 F.2d 301 (2d Cir. 1992).)
and especially
> “The economic effect of a parody with which we are concerned is not its potential to destroy or diminish the market for the original—any bad review can have that effect—but whether it fulfills the demand for the original.” (Fisher v. Dees, 794 F.2d 432 (9th Cir. 1986).)
The "whether it fulfills the demand of the original" is clearly where NYTimes has the best argument.