The Tengu Demon is a monk in a tengu mask who guards Uchitsune's cursed longbow. In the Mythic Tale The Curse of Uchitsune he warns Jin away twice, then duels him once Jin finds the bow.
Picking up the bow sends Jin into a trance. The fight happens in a blood-red arena ringed by crows. When Jin wakes, the bow is his and the monk is gone.
A record on Iki hints he was a victim of the Eagle's poison who chose to guard the bow after seeing visions of doom.