The simplest answer would actually be magic. All of the Eorzean disciplines, whether jobs or classes, incorporate some element of Aetherial manipulation into them. Even the base classes like archer have clear evidence of this with attacks like windbite. Granted, some of them much more obviously utilize arcane powers, like the Dark Knights or the Ninjas, but even the Machinist is based on the manipulation of personal aether. It's part of why the Eorzeans can field soldiers powerful enough to deal with magitek armies, giant monsters and more. It follows to reason that there is an element of aetherial manipulation with the arts of the Dragoon as well, which helps them jump into the air. Also, the game, like many Japanese works of fiction, seems to be based on the power of the self more highly, where one can break human limits through enough training and determination. Given the context of Eorzea, this might involve magic itself.