Biblically, the "King" or ruler of this world is the devil. (1 John 5:19) It also is implied at Matthew 4:8-10, where the devil tempted Jesus by offering him "all the kingdoms of the world". Jesus never denied that the devil had control or the authority over these kingdoms.
Caesar Augustus was the Roman Emperor at the time.
There has never been a king of the world so far - the world has never been that united. The most powerful empire in Jesus's times was the Roman Empire.
When Jesus was born king Herod was king.
Jesus was born during the reign of King Herod.
Herod Antipas was the king during the time when Jesus was performing his miracles.
In the bible the king who was ruling Bethleham was king Herod.
king herod
King Herod II.
Matthew 2.1: Now when Jesus was born in Bethlehem of Judaea in the days of Herod the king,
There is a "king" who is the king of everything which is known as god or jesus. There is no ordaniary man who ruled the world.
When Jesus was born there wasn't an emperor, there was a king, and his name was Herod. He hated Jesus because he thought Jesus had come to steal his throne.
KING Herod
Herod the Great
Jesus came into the world to save the world from sin.