This improv game is in the following improv game categories:
Improvise a simple scene. Then the scene is replayed, from the point of view of one of the characters. You can replay several times, from several POVs.
Make sure the scene is such that the relationships between the characters allow for clear POVs. A scene about dryly buying a pair of shoes does not lead to exciting POVs... Also known as Rashomon. - after the movie by Akira Kurosawa, that follows different points of view as well. For the same reason: Also known as Kurosawa.
The technique can be used as an excellent Narration Exercise : have one improviser tell a story, something simple like what happened to him or her today, interacting with other characters. After that, other players talk about the interaction from the POV of one of the characters in the original.