As far as Purity being the "Khornate" option, of course ultimately everything comes down to the QM's interpretation of the morass of contradictory lore, but I don't think it's a good line up.
The entity or force called Khorne is a volcano or a raging flame, violence and hatred spewed out indiscriminately, destroying anything and everything around it in a cathartic outburst that wipes out enemy, friend, and innocent bystander alike because nothing matters but expressing that hatred and violence. "Khorne cares not from where the blood flows, only that it does."
Khorne is associated with martial endeavors and warriors, but discipline and focus via martial arts, to me that maps more to Slaanesh (see Heresy Era Lucius or the EC's Palatine blades) or Tzeencht.
The example I'd point to on that last one is Iskander Khayon's monologue about the martial tradition of the Thousand Sons in the novel Black Legion, their weaponmasters and elite warriors utilized endless kata repetitions and meditative focus to match their brothers in the less scholarly Legions.