Usually these terminals won't 'decline' a transaction but since they can't handle the chip (but know it's there) you have to insert the chip (and be told it doesn't read it) then you swipe the card and sign or enter your pin.
Bit annoying but you shouldn't be declined
Yes, not declined by the bank technically. But very annoying that these chips cards which were issued by ANZ do not even work on their own ANZ branded terminals. You would think that being an ANZ branded terminal, ANZ Amex chip cards would work seamlessly without having the "chip not supported" message.