Attempting to rigorously define interactivity is about as joyous as rigorously defining the word game into your preferred pigeon hole. You might see healthy debate in this conversation. I see a black hole event horizon through which my will to live is disappearing.
A game is not about walking from A to B, but about the things that happen to the player at A and B - a panorama, a conversation, a moment of madness... The act of walking is often vital to the experience, embedding a player inside the activity in ways that a static image or short film would not.
Joel Goodwin (Electron Dance) on Secret Boxes