The US gates are the E gates. CX uses the D gates. CX888 arrives from HKG at a D gate, and thus departs for JFK from a D gate.
All pax leave the aircraft with those continuing to JFK on CX888 going into the secure boarding gate room. Those connecting to other flights or ending in YVR go to Canadian or US immigration as required.
The JFK pax are rescreened in the gate area by CATSA while pax joining in YVR wait outside. Once the continuing pax are screened, they open the doors for the new pax who are then also screened by CATSA. This is because they haven't gone through the US style screening when clearing security at the international checkpoint (as they would have at the US E gate checkpoint).
CX888 then arrives at JFK T7 as an international flight.

In order to be treated as a pre cleared flight, the aircraft would have to arrive at D69-78 and all JFK pax sent to US immigration while the aircraft is unloaded and screened. JFK pax would have to collect their bags to go through US immigration. They would then have to go to the E gates with doors switched to turn the D gate the aircraft arrived at into an E gate.
Doing all that would require more then the 90 mins they are on the ground.

The International to US directions on the oneworld site are meant for people arriving on CX838, JL18, BA87, BA85 and QF75 and connecting to a US flight (eg, AS, AA, WS, AC).