
Iaido(居合道 Iaidō or just Iai 居合?) is a modern Japanese martial art associated with the smooth, controlled movements of drawing the sword from its scabbard or saya, striking or cutting an opponent, removing blood from the blade, and then replacing the sword in the scabbard. While new students of iaido[1] may start learning with a wooden sword (bokken) depending on the teaching style of a particular instructor, many of those who study iaido use a blunt edged sword (iaitō). Few, more experienced, iaido practitioners use a sharp edged sword (shinken).
This is why the sword is designed the way it is, its combination of both styles of Iaido which how Vergil strikes his enemies in DmC. Also, explains why its slightly out of the scabbard the whole style is about sheathing and unsheathing the blade while in combat. He also uses the sword like a walking cane, so that also kinda fits with the whole aesthetic.