Not only Byzantium, but it is absolutely true about that Empire. Karl the Great Saxonslaughterer didn't think differently, nor did the Czars, Moskau being the Third Rome and the other Christian kingdoms as well.
Steven Runciman says in his book on The Byzantine Theocracy (2004): The constitution of the Byzantine Empire was based on the conviction that it was the earthly copy of the Kingdom of Heaven. Just as God ruled in Heaven, so the Emperor, made in his image, should rule on earth and carry out his commandments ... It saw itself as a universal empire. Ideally, it should embrace all the peoples of the Earth who, ideally, should all be members of the one true Christian Church, its own Orthodox Church. Just as man was made in God's image, so man's kingdom on Earth was made in the image of the Kingdom of Heaven."