There is no narrator in the story, and it is not told in first person as we follow Bérenger's tradegy and he is not telling us what is going on, so the best choice is third-person point of view as the story unfolds and we watch/read the characters interact.
“Rhinoceros” is a play. A play does not have a narrator and the story is told, generally, by the interaction and dialogue between the characters.
However, in “Rhinoceros,” we learn about the history and development of the facts and the narrative, through Berenger's vision. For this reason, we can consider that this piece presents the narration in first person, which is the type of narration where the facts are told by a character present in the story.
