Yes, that is correct. The music video and the novel it's based on are an abridged retelling of the games' story seen from the rival Nemona's perspective. The player character and the girl in the video have the same origin and role. You can choose your name and hairstyle in the games so it's entirely possible to create Anna if you want, they probably went with that instead of using the default name and hairstyle just so it's immediately easy to tell when they're referring to the MV/novel rather than the games.