Unfortunately GZIP won't beat LLMs for text classification. The research you cited is just poorly done science that has been widely debunked. The original paper compared top-2 accuracy of GZIP with top-1 accuracy with BERT. The dataset also contains a lot of train/test data leakage. See this article for the rebuttal: https://kenschutte.com/gzip-knn-paper/ and this thread for a previous discussion on hackernews: https://news.ycombinator.com/item?id=36758433.
Further, the evidence presented by NYT in the lawsuit could be hard to reproduce. I tried multiple prompts on multiple versions of GPT-4 APIs but still could not get GPT-4 to reproduce NYT articles exactly. NYT might as well tried to let GPT-4 reproduce 100,000 articles and only found a few cases where GPT-4 actually recited the whole article. In that case OpenAI might as well be arguing that this is only a rare bug and avoid losing the lawsuit in a massive way.
Further, the evidence presented by NYT in the lawsuit could be hard to reproduce. I tried multiple prompts on multiple versions of GPT-4 APIs but still could not get GPT-4 to reproduce NYT articles exactly. NYT might as well tried to let GPT-4 reproduce 100,000 articles and only found a few cases where GPT-4 actually recited the whole article. In that case OpenAI might as well be arguing that this is only a rare bug and avoid losing the lawsuit in a massive way.