Ryu only appears in a flashback and a dream.
He first appears in a dream Bull had. He then appears in a flashback when he, Bull, and other hunting dogs were chasing down a boar. When they chased the boar to a cliff face, Ryu charges at it, ignoring Bull's orders to wait until their owner arrives. The boar grabs him by the front paw and was shaken until Bull saved him by attacking the boar. He wasn't seen ever since.