This has been my experience since I first flew into Chek Lap Kok with my parents in 2001 even when having a economy or business class ticket (with BA, CX & Qantas).

Arriving into HKIA, if in a wheelchair usually escorted through the staff channel (flight crew exit) far left, security come out, the escort would show their airport staff pass to security, then security would look at your passport or HKID, takes it into a side room then gives it back and opens the security door, you then go onto the baggage area.
If visibly elderly (some people do not look their age) or with young children you are asked/invited to go to an empty security gate/position so you do not have to queue up with everyone else who came off your flight.

Departing HKIA, when my mum needed a wheelchair, after checking in we had to wait for an escort and a wheelchair, the escort took us through the departure/security area, to the far left was the staff channel (flight crew entrance), the escort would show their airport staff pass to security, then security would look at your passport, takes it into a side room then gives it back and opens the security door/gate, you are then invited to join an empty or smaller queue for hand baggage check and overall body check.
When we had our own manually wheelchair we were asked/invited to go to an empty passport check gate/position and then invited to join an empty or smaller queue for hand baggage check and overall body check.