It already is in so far as it's a medium for creative output. I think when a lot of people bring up the topic, they're more wanting to be able to put gaming on some sort of pedestal of high culture, which I'm not entirely sure games have reached yet.
While there have been some decent stories in games, they still need to be qualified as "being good as far as games go" but don't really hold up compared to the best that film and literature have to offer. I'll take the works of Hardy, Dickens, and Proust any day over the best stories to make their ways into games.
Even from a visual standpoint a lot of what seems to be pursued has been greater and greater levels of photo realism. There've been a few exceptions from major developers who have gone for something very different (prime examples being Okami or Windwaker), but it's largely indie developers in the last few years that have really tried to break the mold in terms of bringing new, unorthodox visual aesthetics into gaming (Fract and Antichamber, for instance), so I do see things improving in that regard.
There is one problem that I think has yet to be hammered out, and I don't know how the industry would go about it. I remember seeing an interview with Frank Zappa years ago where he was criticizing the direction mainstream music was heading, and he felt that people were more concerned with making a product than with making art, and I do think this is something that the game industry suffers from. Any facet of a game seems to be whittled down to a bullet point that the producer's PR team prattles on about ad nauseum, stripping away any joy that it may have brought, making it feel almost sterile after it gets chewed up by the company's marketing machine.
Personally, I think that it's important in a creative endeavour to think, "I'm fucking doing this, and to hell with what everyone else thinks." It could be amazing, or terrible, but when it's good, it tends to be brilliant, and can bring about a whole new movement in whatever corner of the creative world that it sprung up in. Granted, this is a lot easier to do in the realm of painting, literature, or music, as the financial barrier to entry isn't all that daunting. However, games are inherently more expensive to put together.
As such, the people behind them probably aren't going to be able to self-fund their project, and need to look elsewhere for capital, be it a publisher, or crowd funding. At that point, they're forced to treat their game as a project that is worth investing in. A publisher will want a decent return on whatever they give the devs, and even stuff like kickstarters see people who threw money at different projects demanding more and more say into the direction it is taken. With that, it strikes me that developers can't be 100% free to indulge in their own artistic freedom since they're beholden to one paymaster or another to even get their game completed, and prevents them from fully expressing themselves, forcing their game to be more product that art.