My interpretation of prior mechanistic interpretability research is that LLMs transform concepts in non-verbal spaces as well, which is why that was a surprising statement. For example showing how they do arithmetic on line lengths by rotating helical manifolds.

And the way they transform data isn't by transforming words. The layers transform high dimensional vectors - a format very alien to us. It's not obvious that these vectors must encode concepts from the vocabulary.

Edit: the paper claims that it's only J-space concepts that need to map to English words, other forms of cognition that are more 'practiced' and don't require so much reasoning bypass the J-space and can work in non-verbal subspaces. So that's the answer.