The complaint isn’t that ChatGPT is imitating New York Times style by default.
The complaint is that you can ask it to write “in the style of New York Times” and it will do so.
I don’t know if this argument has any legal merit, but it’s not as simple as you suggest. It’s the textual parallel to having AI image generators mimic the trademark style of artists. We know it can be done, the question is what does it mean legally.