'Pirate King' has the same kind of setting (desert) as 'Treasure' which suggests it's before or after the 'Treasure' Music Video, since 'Say My Name' has to come before 'Pirate King' and it merges into 'Treasure' but 'Pirate King' Has to come right before or after 'Treasure' it only makes sense it's right after.
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Ateez MV timeline theory
RandomThis is a fun quick thing where I try to make sense of the Music Videos of ateez.