Australia is the world's largest island at 7.9m km² ... Not sure why they're trying to say Greenland is larger.

They aren't trying to say Australia is smaller. They sought to exclude it by saying it was the biggest of "non-continental" islands.

Antarctica is a larger “island” than Australia. But both are also continents, while Greenland is not (yes, this is rather arbitrary labeling, but it is what it is).

> yes, this is rather arbitrary labeling, but it is what it is

AFAIK continents are based on tectonic plates.