Was having a look at some of the benefits with my new NAB card and they had a link for www.amexconnect.com.au
It's a quick sign up and seems you click through to the winemarket offer to get the $60 off.
Probably you can log directly into winemarket.com.au and use the code AMEX60 as well.
Confirm that I was able to use the AMEX60 discount logging directly onto winemarket.com.au and I then paid with Paypal + credit card. Shipping expensive at $16 a doz. but still cheap overall. Good find OP….:-)