This part of the passage stuck out to me also. My read on it is that what enables the subject of the story to guide his knife so well is: human attention is a finite resource and it's typically divided up among many things, and, the more attention allocated to something the more rich its representation in consciousness.

If you have some variation in success watching your breath in meditation, you'll notice an astonishing range of detail that your breath might be represented with. When you are distracted, it might barely register as the symbol, "feeling of breath"; and if you have nothing else on your mind, you can have a super rich, fully continuous experience of it moving in and out, with all the gradations of temperature at different points etc.

Seems not very useful with breath watching, but if you carry this over to a sport or other skill, it's amazing how much more time it seems you have to act, and how many subtleties about the playing field that are otherwise totally filtered out.

I can imagine the butcher feeling every little difference in density of the meat as his knife moves along, anticipating where it will give or catch and always remaining on a smooth track.