And blurred lines like you illustrate above are a good argument why we can't say video games should be primarily considered performance art pieces in the realm of interaction design, as well as why we can't say video games should be primarily considered story delivery mechanisms.
The video game is both interactive and passively consumed.
Machinima exists because of how enjoyable experiencing a story through a video game environment can be. Spectating video games is a Billion Dollar Industry (TM), with Twitch and international professional gaming leagues getting ESPN coverage.
There's value in the mechanics and human interaction as story, on one level, and the fiction in the game itself as a story.
As well there's value in how the interactions make us a part of the game and a part of the story. Sure I know I'm not the lovable Italian plumber, but after a while my brain stops making that distinction, at least a little bit. I know I'm not a Guardian defending the remnants of earth from big brutish aliens, but after a while I stop consciously identifying that barrier, letting it become translucent.
The closer and closer we get to immersive 3D gaming, the blurrier that line becomes. So there too ^^, the story is incredibly important as a driving motivation to play and enjoy video games.
And really... the closer we get to putting the human inside the game, the more important that story is going to become. The interaction mechanics are important because when they're done right, when they're executed beautifully, we stop thinking about the game and form a more consciously transparent symbiosis with the technology. The COD games were fantastic because the FPS controls Just Worked.
What happens when we continue progress and get to neural interfaces, where the designer builds a realistic-enough-feeling environment that you can engage with the characters and elements in it? Story, I guess.
So... to summarize too many words for a simple counter-point: it's all a part of the whole, and inappropriate to say games are just a subset of interaction design.