The term translated here as “kingdom” denotes not just the geographic area over which a king rules; it denotes also the kingship itself, and so describes who is the sovereign over the world. The term translated as world
describes God’s creation as fallen and so is the realm Satan had claimed for himself (Luke 4:5).
15 Then the seventh angel blew his trumpet, and there were loud voices in heaven, saying, “The kingdom of the world has become the kingdom of our Lord and of his Christ, and he shall reign forever and ever.”