copyright only protects them from people republishing their content

This is not correct. Copyright protects reproduction, derivation, distribution, performance, and display of a work.

People also ingest their content and can make derivative works without problem. OpenAI are just doing the same, but at a level of ability that could be disruptive to some companies.

Yes, you can legally make derivative works, but without license, it has to be fair use. In this case, where not only did they use one whole work in its entirety, they likely scraped thousands of whole NYT articles.

This isn’t even really very harmful to the NYT, since the historical material used doesn’t even conflict with their primary purpose of producing new news.

This isn’t necessarily correct either. I assume they sell access to their archives, for research or whatever. Being able to retrieve articles verbatim through chatgpt does harm their business.