I believe it has some reference to the Priene Inscription (
https://en.wikipedia.org/wiki/Calendar_Inscription_of_Priene). Augustus was called "The Savior of the World." He was worshipped for bringing peace to the world. The Priene Inscription reads, "The birthday of the god [meaning Caesar] has marked the beginning of the gospel of the good news for the world." It talks about Augustus making wars cease, and creating order everywhere.
When the angels showed up that night, they basically quoted the Priene Inscription, but Augustus was not the subject of it—Jesus was. It was a messianic challenge to the throne of Rome and everything it stands for, as a symbol of the world.