Onitama

Main character lives alone after his parents' death. Neighbor woman serves as his guardian. Protagonist can see demons invisible to the ordinary eye and begins to feel another entity inside himself. One night his ability calls him to the night school where he almost gets killed by a devilish monsters. A mysterious girl with a sword defeats the monster and saves protagonist's life. He learns that he is destined to fight and devour spirits.

[From vndbreview]