That clip just sounds like 'Woman Tone' to me. The amp and rolling the tone off can make that sound with lots of pickups in a Les Paul, as long as the pickup is also bright to start with (you can hear some bright snap to the tone through the darkened wooly EQ on it.). The 'squish' in that attack typically comes from a tube rectified amp, though an A2-based pickup might have some of that to it (but not all A2 pickups do - Pearly Gates are an exception, they are brighter and tighter than any other A2 based pickup.)
A 59n, PGn, APH-1, WLHn all could make that tone, with slightly different amp and guitar tone settings. A 59n/A4, PGn would be my first choices. WLHn or APH1n would be my second tier of choices.