Honestly, I think the entity is a fairy associated with owls and wants to kidnap the player. In "See you in x" and "Spoilsport" feature a fae-like entity. Taking eyes seem very fae-like to me. The "Candidate" and "See you in x" implies that the entity is planning to kidnap/indoctrinate the player and using the quiz to scout out their next victim. "Spoilsport" also implies that the entity also views the quiz as some sort of game which falls in line with the fact that fairies are also depicted as having different morals than humans.
that's interesting. I like that idea, but there's also the "I am"-"angels are" and a few other references that make me think that the entity is a fallen angel-like creature, but I also like the fae theory. And associating it with owls makes a lot of sense, because 1) Owls have large eyes and good vision, which would tie into the whole "stealing your eyes" thing 2) There are a few pictures next to the quiz with owls. I like your theory!
Another thing I noticed: There is an ending called "Friend". I was aware of it at the time(because of the credits) but I haven't actually seen the ending screen. Someone else in the comments got that ending and it said that the entity is planning to transform the player. The existence of the "Friend" implies that there is a difference between it and "Candidate".