In my opinion, the vast multitude of different animal intelligences is a clear hint that language does not an intelligence make. We're animals, and our intelligences did not come from language; language allowed us to supercharge it. We can and do think and make decisions without using language, and the idea that a statistical model based solely on our language can be intelligent does not follow.
The point of the book is that we've been very bad at testing animal intelligence because of a vast stack of human biases, including things like language and the geometry of our hands.
Animals with different geometries and no language are still intelligent, but we need to test them in ways which recognize their capabilities. Intelligence is general: it's adaptivity within one's set of constraints.
De waal also points out that there was massive shifting of the definition of language and intelligence as we became more aware of what animals are capable of.
From this angle, I would say that LLMs are intelligent: they do adapt to their inputs extremely readily, though they have a particular set of constraints (no physical body (usually), for starters). They are, like chimpanzees, smarter and more capable than humans in some ways, and much dumber in others.
Finally, the 'statistical learners can't be intelligent' line of argument is extremely short-sighted. Our brains are bags of electrified meat. Evolution somehow figured out a way to make meat think. No individual neutron is intelligent, yet the collection of cells is. We learn by processing experiences with hormonal signals because those hormonal signals are what the meat is capable of working with. LLMs, by contrast, learn by processing examples with backprop. If anything, the intelligence of meat is more surprising.
Language is just the input/output modality.
In any case though, if language is just the input/output modality, where is the intelligence when language is not involved? Is the "intelligence" of ChatGPT/Claude/Gemini models dependent on the human-decision-curated linguistic dataset they have been trained upon, or is it prior to that? If a SOA LLM were to be trained on the same dataset as them but was not in any way put through RLHF for it to respond to human prompts, would it be intelligent? What would be the expression of that intelligence?
I'm not sure the word "intelligence" really fits what these models are doing. I do however think it's safe to say that they are performing cognition - even if it's 'simply' cognition over their provided context and even if it's entirely limited by their training set. We still have a machine that can perform automated cognition over a increasingly wide distribution of data.