Interaction accomplishes the browsing of information, just like scanning a picture or looking through a card catalog.
And when folks make broad appeals to interactivity, they are saying that somehow the interaction of the gamepad is fundamentally different from turning the page of a book.
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.
It is the simulation that people turn to next - a believable world that responds to your actions in complex ways.
But again, there is a problem - more than one problem. If the simulation is as chaotic as reality, people lose track of the hooks that kept them involved - they no longer have the ability to make extensive plans or strategies, neither are there any puzzles to solve cleanly and gracefully. And if the simulation adds detail without purpose, it dilutes any designed intent. The small differences in situations are vastly overwhelmed by a few key elements that control the real outcomes - leading to a noisy experience. Only a few kinds of games can survive the extensive sim treatment - the kinds of games that you play with the intent of telling a story about later. Put to this purpose the details rise back to the surface as important story elements.
If not those two things, what is it that is grabbing you about Starcraft? Here I would pause to consider what unifies chess, science, and literature. It is the conversation of being posed problems and arguing your case and proving your points, given a factual situation involving arbitrary rules. There are different interactions involved in each case, different skills and levels of execution needed. But it is this thing of being posed interesting problems with variety, one after another, that drives both the best liked games and stories. They don't have to be hard or deep problems - "who will the main character hook up with" drives countless stories and "which team will get the most points" drives most sports - but they give you something to chew on.
And so a writing focus is, in this light, an equal partner to a mechanics focus - either could be taking the lead role. The writing could pose a question that the player solves mechanically - that's a very typical model. Or the writing could usher you in one direction, only to reach a mechanical contradiction, leading the player to a critique of the system, a desire to escape the rules.
What we don't ask people to do in games is to design, from scratch, large parts of the experience. That takes us out of the realm of immersion, browsing, and strategizing, and into "hard" creativity where an intentional vision drives large bodies of work.