That is not what I have read on the Australia and New Zealand websites. Your link is dated last July.
https://www.health.gov.au/health-alerts/covid-19/international-travel
COVID-19 testing
From 12:01am on Thursday 5 January 2023, people travelling to Australia from China, including Hong Kong and Macau will be asked to show evidence of a negative pre-departure test for COVID-19. Read more about the COVID-19 testing requirements for travellers from China, Hong Kong and Macau.
If you are arriving from other destinations, you do not need to provide proof of a negative COVID-19 test to meet Australia's travel requirements. Some countries, airlines and vessel operators may require a pre-departure test result at check-in before you can board your flight or ship. Check the entry requirements of the country you are travelling or transiting through, and your airline or vessel operator’s requirements.
Visit the Smartraveller website for more information.