When the Church calls Jesus the "King of All Nations," she does so with various prophecies of the Old Testament in mind.
The current translation of this antiphon is as follows.
O King of all nations and keystone of the Church:
come and save man, whom you formed from the dust!
The prophet Isaiah refers to the Messiah as a judge of all "nations."
He shall judge between the nations,
and shall decide for many peoples;
and they shall beat their swords into plowshares,
and their spears into pruning hooks;
nation shall not lift up sword against nation,
neither shall they learn war any more.
The prophet Jeremiah is even more explicit in his reference to God as the king of all nations.
Who would not fear thee, O King of the nations?
For this is thy due;
for among all the wise ones of the nations
and in all their kingdoms
there is none like thee.
Daniel is another prophet who looks to the Messiah as a king.
And to him was given dominion
and glory and kingdom,
that all peoples, nations, and languages
should serve him;
his dominion is an everlasting dominion,
which shall not pass away,
and his kingdom one
that shall not be destroyed.
The people of Israel were looking forward to a messianic king, whose reign would extend to all the nations. Theses and other prophecies find their fulfillment in Jesus Christ.