I can't find any lawsuit between News Corp and Google. In what country? Google did agree to some kind of paid agreement with News Corp in 2001, according to news coverage at the time in part to avoid the threat of legislation in Australia that might have required Google to pay for content to index it. (No such legislation was passed in Australia, let alone the USA).
One USA case from back in the day that ruled that Google Indexing (and caching) was fair use, was Field v. Google, from 2006. http://www.eff.org/IP/blake_v_google/google_nevada_order.pdf
Another USA case that ruled that Google Image indexing, and using thumbnails in search results, was fair use was Perfect 10 v. Google (2007). https://cyber.harvard.edu/people/tfisher/IP/2007%20Perfect%2...
It's true it hasn't been super extensively litigated, and never made it to the supreme court. Perhaps because in fairly short order content owners realized they actually wanted to be indexed in google. And because Google (if not everyone) would respect a robots.txt to keep them out if they didn't.
The Google Books case is also probably relevant. (Which Google also, eventually, won).
There are other cases not specifically involving Google that are relevant, one for example with an index of tv news broadcasts that provided keyword search and let users view clips. The court ruled this was fair use too. Fox News v. TVEYES, Inc., 43 F. Supp. 3d 379 (S.D. N.Y. 2014).
I don't think I can find any USA cases that suggest indexing for a search engine would be a copyright violation and not fair use. Let alone against Google specifically. When you say courts have ruled against Google, can you cite any particular cases? Maybe they were from other jurisdictions than USA? Or cases relevant to this present topic even if not about search engines?
And yet, GP's description applies just as much to google indexing images. Google makes money off of a search index that copies copyrighted content without explicit permission or compensation. Still, you are right that other factors may be different; it requires an argument that goes beyond GP's, and is actually based on the law.
In the USA, where OP suit is filed, I am not a lawyer and this isn't legal advice, but I think these image AI's are going to have a pretty good case for fair use, even if it what they did counts as "making a copy" (which I think isn't totally clear). It is a very transformative use. I think convincing a court that the AI's will result in lost revenue (for the specific works used as training data, not in general for the field) would probably be necessary, but not sufficient, to overcome a fair use defense -- and I don't think that argument is even a slam dunk. And is still just one factor in fair use; the transformative nature of the use has lately been given a lot of weight in the law, and seems pretty overwhelming here.
Of course, sometimes courts do surprising things.