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Taylor Swift 's giving her fiancé, Travis Kelce , a pretty impressive birthday gift ... she's putting out a whole music video all about the song everyone thinks is about their romance!

The singer-songwriter just dropped the vid for "The Fate of Ophelia" -- a song in which she likens herself to the character from "Hamlet" ... and, she credits Kelce for saving her.

The video starts in a hotel ballroom ... with a mural of Taylor as the doomed Shakespeare character on the wall -- before taking fans through a series of smoky jazz clubs and movie sets.

Swift fights pirates atop the bow of a ship in one scene, dons an old-school swim cap in another -- and even ends up in a bathtub, the water rising up her face. The character Ophelia famously drowns herself at the end of the Shakes

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