This is as been explored in the FPS genre for a long time, I would take Half-Life, Far Cry 3 and BioShock as clear successful examples of this concept. But it's always been limited, in the sense, that the space between the screen and the user always established a clear physical distance between the player and it's avatar.
That's one of the core tipping points of VR narrative design that it will differentiate it from traditional interactive experiences. So now interactive narrative designers can now truly explore the concept of having the player act out the scene as being part of it.
The physical leap between the eyes and the frame of the screen is gone, what's happening outside of the player's view is as important than what's within it. And because in VR, the space that surrounds the player is actually felt and constantly present in the experience.
It's really the end of the "frame", the concept of the window to the world that is so core to classical medias like TV, film and the web. We now need to think in terms of space and "self-projection".