The plaintiffs are claiming that their art-style is copyrighted intellectual property and that they can sue image generators for damages if it creates an output that resembles theirs. Regardless of what you think about AI art, the precedent of this case will be a huge expansion of the power of IP and copyright law in the US mainly to the benefit of corporations - imagine Disney copyrighting the look of their 3D anima…
That's not what they're claiming. They're claiming that the models were trained on copyright material[1] and that training models doesn't constitute fair use[2]. Their claims are in the first couple of pages of the court ruling. The claim is not that the style is copyrightable but that producing work in the same style could affect the market for the original product which is one of the parts of the four factor test f…
That said, their trade dress claim doesn't go so far to claim ownership of an entire style, it is the use of that style in association with their names that is the problem. For example "draw a stick figure cartoon dog" is fine but "draw a dog in the style of xkcd" is not, by their reasoning. And you certainly can't advertise that the model can make images in the style of these artists in ways that might be interpreted as the artists being involved with the company.