There likely isn't a definite reason, but here's my theory:
Not all Pokemon that levitate are Psychic or Flying type. For instance: Victreebel, Magnemite line, and Kingdra, among others. Darkrai is a being of immense power, so it is entirely possible that it's able to use a little of that power to hover.
Another slightly illogical bit is that it can learn Ominous Wind. Maybe this wind is so strong, it's able to push Darkrai off the ground. This doesn't make as much sense as the first theory, however.
Of course, it's completely Game Freak logic until they tell us why.
Hope I helped!