The merchant-specific offers are advertisements purchased by those merchants. This offer is from Qantas, not from American Express. It stipulates that the ticket must be purchased on the Qantas website. This means Qantas won't have to pay a travel agency commission, and they can use that savings to help offset the cost of the offer.
Something about our account activity or other demographic criteria (known to American Express) tells them that you and I are the type of people who might travel to Australia. Like you, I have intention to go. (Although, ms
mia has been suggesting this for years, but I don't think American Express would know this unless there are audio chips in our cards
).