I've thought pretty hard about this as well.
I do not think that video games are really viable as "art," in the traditional sense. The very facet you deem it's strength -- interactivity -- obliterates any chance of such.
But that doesn't mean it can't be something awesome, intelligent, and sophisticated -- it just won't be art, in the traditional sense, where meaning is conveyed by the artist(s), and not by the viewer/audience. So while I'm being rather technical here and saying it can't be "art" on a purely semantic level, it still could have all the qualities that we associate with art: significance, intelligence, and sophistication.
And I totally agree that interactivity is the key to achieving this. Games that stress interactivity will be the key, which is why I think something like "Oil God" or even "The Sims" comes much closer to being Video-Games-As-Art than, say, Final Fantasy does: a game that almost deliberately limits interactivity and open-world in order to tell a linear story.
Instead of ruthlessly supressing interactivity in the name of storytelling, I think games should embrace their interactive side; a game-as-story is just a crappy movie. In fact, one could use this truth for almost any serious medium -- should movies engage in extensive, heavy internal dialogues? Limited use is fine, but it simply isn't a strength of the medium like it is for books. The strengths of movies (over books) are their visual and audio stimulae. This is why great novels with extreme amounts of internal dialogue (such as Brothers Karamov or Crime and Punishment) have absolutely never translated well into film, while novels that have focused more heavily on external dialogue such as Pride and Prejudice or even Shakespearian plays (no, these aren't actually novels) translate much more readily and succesfully.
Every medium has its strengths. Clearly, the unique and defining feature of video games is its interactivity. The games that supress that interactivity -- such as Final Fantasy -- are the antithesis of this goal. Because it's such a popular series, Final Fantasy has become a symbol to me of what gaming should not be: crappy movies with some interactivity, rather than something that's interactive first and foremost.
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