Imagine the tension on that guitar neck; maybe the truss bar is made of titanium. On electric guitars these extra strings are bass, e.g., F# B (followed by E A d g b e). Some accoustic eight-string guitars I believe have at least one extra treble. In the piece above as Conti plays solo, before the bassist joins in at 1:09, those deep extra basses almost sound like a regular bass guitar.
Whether Conti’s playing an eight or his regular six-stringer I’ve never seen such effortless fingering from any other guitarist.
Robert Conti is my favorite jazz guitarist (his fingers effortlessly perform every nuance of a melodic/chordal phrasing) There’s a lot of Conti videos collected at this Youtube master page
By the way, here’s Robert Conti back in the year of 1969 playing a classical guitar finger style: