Escaping from prison into a dark and dreary night, adrift in the desert, this troubled soul is fleeing more than a state institution. He wants to "run away" from the guilt, confusion and fear of whatever it is he's done - or is at least accused of doing. But he doesn't need to look in the rear view mirror to know that these regrets will not be leaving anytime soon.
In David Lynch's Lost Highway (an obvious influence here) Fred Madison suffers from a psychological "fugue state." This means that Fred creates in his mind a fresh identity (full of new people, places and memories) and proceeds to forget his true self. Yet like the crazed driver in this Daughters' video, Fred can't really erase his memories and begins to subconsciously repeat or relive his mistakes. In fact the protagonist of "Plaster Casts of Everything," who imagines a strange woman in his passenger seat, may very well be haunted by the same guilty demons as Fred - that of his wife's murder.
A fugue also happens to be a style of musical composition, one which features multiple parts that come together in a sort of circular form (returning to the opening key). The Liars' excellent single doesn't necessarily follow that style, but there is a connection between the repetition of the pulsating music and the building tension on screen. The final coda implies that rather than an endless cycle of shadows and desert, things may actually get worse for this guy. He's caught in his own nightmarish spiral of horror and self-hatred - and there's no going back.