Just finished playing Dear Esther

[Damascus Rose]

Yes, and this game has interactivity. Walking is interactivity, therefore it is a game. You are in a virtual world using a mouse and keyboard to traverse through it, making your own choices on what to look at, where to walk, what to zoom in on. It is a game by the definition of the word. Whether the interactivity may be limited or not, it still exists, and you cannot deny that it does. Whether the effect could have been achieved using rails is besides the point.