I think that the common meaning of AI has changed since this was written. This book was written at least 14 years ago, long before anyone had heard of an LLM. Matt Mahoney incorporated neural networks in his compressors. Afaik they weren't pretrained. They were adaptive and made one pass over the plaintext, simultaneously learning and predicting. Decoding worked similarly.
If you go and (re)read what he writes in relation to AI, which I just did, it's about exclusion. He excludes "Universal Compression" as impossible, Kolmogorov compression as uncomputable, and then he gets to Artificial Intelligence. Artificial Intelligence is an appropriate way to model data, since data is created by humans with human intelligence. And, AI doesn't violate mathematics the way Universal Compression and Kolmogorov solutions do. So therefore, Artificial Intelligence is what's left. That seems to be the argument.
When decompressing, you need to reproduce the output of the LLM exactly as it was during compression, otherwise the decompressor would output gibberish. Can you count on the LLM being that consistent?
Fabrice Bellard did something with neural nets and a transformer model [1] that was very successful.
I suspect that LLMs wouldn't be ideal to use as compressors, because they are large, consume a lot of resources, and are constantly changing. You need the model to produce exactly the same output at encoding and decoding time, or else you get gibberish.
I think they also make money from people that don't know the difference and use it because, for instance, it's the default in Edge when you search from the URL bar.
I started learning Common Lisp, but ASDF and Quicklisp threw me off. I couldn't tell if you were supposed to choose one or the other or they were used together. This might revive my interest in Common Lisp if I get around to reading it. But in the meantime I drifted off to Racket, which is relatively well documented and has extensive libraries and really unique features.