The novel parallel is a great one. Novels, like games, are not passive art or entertainment. The reader has to keep turning the page, moving left-to-right through the world the author has created.
I can certainly agree with you that writing can have a meaningful impact on a game, but it's not the reason a game becomes art, as this Polygon piece would have us believe about StarCraft. StarCraft is absolutely an example of how interaction is the core of the experience, and writing only helps construct a narrative to draw you into the experience, providing a cohesive metaphor to describe the experience - both during and afterward.
Like Mario saving the Princess or Donkey Kong collecting his bananas or Terran defeating the Zerg, whatever goal the game designer creates to propel you into the narrative is orthogonal to what ultimately makes the experience meaningful. The first Goomba in Super Mario Brothers is far more important to the experience than the Princess at the end of the game. Hell, the first question mark block is even more meaningful than that.
But you're right, that without the eyes on the Goomba or the question mark on the block or Mario raising a flag at the end of the level, there's no narrative to be drawn into, there's no way to describe what you're experiencing.
And you put it so perfectly:
But that isn't what we are thinking about as we get immersed in a game experience - we soon forget that the controls are there.
In a great novel, the words fade away and the book disappears and all that remains is the dream world the author has written for you.
A game does almost exactly the same thing, but through action and feedback. The feedback can be text, voice over, artwork, animation, or any of the thousands of possibilities digital multimedia has opened up for us, but it should never try to be meaningful unto itself. This is where game designers get bogged down in trying to be like other mediums. Feedback is about rewarding the gamer's action and pushing into the next action, looking for greater reward. A mushroom comes out the question block, the old man gives you a sword, your wave of zerglings wash over a gas refinery.
You might argue that writing is key to creating this experience, and I won't disagree, but the Polygon piece absolutely fails to illustrate this, and so another wave of English majors says to themselves, "Well, if I can't get my novel published, there's always video games"