The NYT needs to increase profits every quarter, just like everyone else. I have no doubt they will license their content to OpenAI. With the issue unsettled legally, right now, I suspect the NYT doesn't think OpenAI is offering them a fair deal.
Privately controlled companies need to do what their controllers think is most important. If the Sulzbergers think taking a stand on AI is more important than profit, they can go a long time without increasing profits.
The nyt isn't taking a stance against OpenAI. This is simply a negotiating tactic to get money for licensing
We don‘t know their personal motivation. They may very well dislike AI.