It's been a long time since I read Hofstader's book "Fluid Concepts and Creative Analogies" that this is presumably based on, so I'll be interested to watch the video as a refresher, later. :) He also wrote a follow-on book, "Surfaces and Essences: Analogy as the Fuel and Fire of Thinking", published after this video was made, that I've never read.
From what I recall, to Hofstafer analogy making isn't some higher level cognitive process, certainly not a language based one, but basically is THE cognitive process all the way from perception on up, and is the mechanism by which we form object categories in the first place.
As always Hofstader's ideas are interesting, but I can't say I agree with them. It seems that the key evolutionary benefit, and function, of a brain is prediction, which is the superpower that moves us from being stuck in the present to being able to "see" (predict) the future, and therefore from being merely reactive to being able to proactively plan and predict future outcomes (what will the sabre-tooth do, where is the water supply?) based on our experience.
Given the never-same-twice nature of sensory perception, before you can predict you need to be able to generalize/categorize, which I think Hofstader would regarded as analogy making (how is this thing I'm seeing similar to what I've previously seen?), although it seems the actual mechanism involved is embeddings or embedding-like representations where similar inputs have similar representations, and what might more simply be considered as associative recall provides the generalization from view/instance to identity/category.
So, is it really analogies all the way up, or are our perception and cognitive processes better regarded as generalization and prediction, which seem not only seem to have direct and obvious neural realizations, but also match the evolutionary needs that we would expect to exist?
Ironically, I think he was right! In fact some of his initial experiments, like copycat, were about predicting patterns. You can see next-token-prediction from there. But I think he always held out for an algorithmic/logical method rather than a purely statistical one.
If he had accepted the "Bitter Lesson", I think he would have been at the forefront of LLMs.