I'd hazard that he means "style" as a deliberate mannerism, while what he's talking about is "phenomenological extension" -- a feeling that the machine and process have become part of the physical body (a simple illustration of the process -- imagine how you "feel"the road when driving).
Lack of this connection is, imo, the biggest problem with the modern generations of electronic cameras. It disconnects your hand from the physical process.
Mechanical cameras like the Leica are just the opposite, very tuned to the hand. Gibson's physical/mental process, however he imagines it, is probably pretty transparent to him -- the hands know where to go and what to do and the entire process gives him the result he expects -- he doesn't worry about anything to get that imagined pic onto the film. This is different from "style" and not unlike Miles Davis's explanation about some of his music (quoting from memory here): "I'll play it, and then you let me know what to call it."