The Big Book o'Bullets (Cartridges of the World) has interesting things to say about it.
It's a modified .577 Nitro case and was created by Ross Seyfried. ("Nyati" means "cape buffalo" in several African languages.) Top loads will exceed 10,000 foot-pounds, and the recoil is in excess of 150 foot-pounds in a 10-pound rifle with muzzle brake. (They say it's like dropping a 10-pound rifle off a 32-foot cliff and catching it with your shoulder.) Most common bullet weight is 750 grains. The .50 BMG has more steam, since it throws bullets of the same weight 300 to 400 fps faster, but the .50 is not generally chambered in a rifle-sized package, while the .585 Nyati will fit any magnum-length Mauser action with minimal modifications.
COTW says that this is most likely the world's most powerful shoulder-gun cartridge.