Here's a quote from a Q&A with Vivek:
"I want to basically play a new brand of position-less basketball. I want to have these super-athletic, young guys that can run and feel out the game. Guys like
Rudy Gay, and
Derrick Williams, these are
guys who can play the 1-2-3-4 positions."
Regarding
Demarcus Cousins he says that boogie is a mismatch on the floor,
too big for smaller guys and
too fast for the bigger ones.
"He represented the 21st century player that I talk about."
http://espn.go.com/blog/truehoop/post/_/id/67010/qa-kings-owner-vivek-ranadive
So I think it is about versatility and creating mismatches. In the half court they try to be like the spurs, share the ball and play good defense (see Summer League) and try to use mismatches. And whenever there's a chance get out and run. But I don't think it's run'n'gun, more like a more athletic spurs team where the players are able to create mismatches because of their versatility or if you will their ability to be positioneless