In a series where monsters appear and disappear out of thin air, in a series full of powerful magic which does not incinerate (or freeze, electrocute, irradiate etc.) mere mortals, in a series where moogles and chocobos exist... I'm pretty sure jumping abnormally high is pretty low on the list of peculiarities.

It is obviously the power of l'cie. Or, something. It's just video game logic.