No wonder you are confused!

At the time of booking online you would have been asked the the question .... 'is the payment card holder travelling on this booking? ' .... to which you should have answered no.
This has the effect of setting the booking up as third party which over rides the requirement for payment card to be presented at the airport.

Providing you correctly indicated that the payment card holder is not the travelller then card will not be required at the airport.