A Second Person

Yet still others, the literary critics, noted that unlike novels, video games and film have never had the second-person perspective, the "you." Cameras in video games often take the point of view of a character's eyes and ears (first person) or take a vantage either above or behind (third person) the character, as a drone's-eye view of things. While true, they said, that players often get a vague out-of-body feeling during games and will duck if Mario's head is about to hit the ceiling or will turn their bodies when their go-kart needs to turn a corner in a race, this does not mean that they are Mario or are the go-kart. It means merely that they can empathize with or ally their consciousness with virtual objects like Marios or go-karts.

I think a second person game would be a first person game where you got to create the character and interact the way that you would like, instead of acting as an already created character, which would be the first person.

House, P. (2022). Nineteen Ways of Looking at Consciousness. St. Martin’s Press. p. 56