The issue doesn't appear to be that the Australian gov want the horrible video to be blocked just for Australian Twitter users in Australia, which Twitter had agreed to do, but also have it blocked world wide.
Now on this occasion the video sounds to be something that shouldn't be available to view on social media anywhere and Twitter should remove it on the grounds of decency, but I can also understand why Twitter is fighting against a government trying to use their laws to demand a world wide block.
As if the AU gov are successful in their national law affecting what everyone can view internationally, then what is to stop another country passing their own local laws that mean social media posts they find objectionable also being removed for everyone.
An example is if a whistle blower was using social media to bring up human rights violations by a regime, would be want a country to be able to pass a national law that made social media companies legally required to remove all posts world wide that criticized that government?