There is mention of 018/176 but that is reference on how to book if ticketed in QF/EK.
I reiterate the following:
Chauffeur Drive is only available in selected locations to customers holding tickets with confirmed reservations in First or Business on eligible Qantas or Emirates operated flights.
That is the only qualification I can find.
Please indicate where it is specifically indicated that passengers travelling on the eligible flight numbers in first and business but not ticketed with EK/QF are
not eligible for the complimentary service.