Well, defining art is very shady subjet, especially because 'art' is always defined differently in history and by different people. For instance, a painting with a large black circle is considered a masterpiece while a children's fingerpainting, which could be more artistic, is considered a low form of art. In fact, movies were not considered an 'art' until it held more prestige during the 1920's or so, so in many ways, video games are battling up the ladder in much the same manner as movies did way back when.
However, I believe a craft is an art, and that design is an art. Game design, much like fashion design or architectural design, is about functional art. It may seem as though it's meant purely for profit, but there's a lot to be said about artistic vision and molding the mechanics of a game so that fit in with the aesthetics that both the developer and publisher believe the gaming audience will respond to.
Truly, if art is a personal expression, then you can find that in games. It's not spoken about a lot because individual auteurism is trumped by company auteurism in the game industry, but there is a difference between games developed by Miyamoto and those made by Cliffy B. Of course, like animated movies, companies can become the artists themselves - Pixar, Disney, Studio Ghibli, Industrial Light and Magic. So video games, which are digital by nature, can be seen that way as well. There is an artistic difference between RPGs made by SquareEnix and Level 5.
For video games, art is found by how the mechanics of the game blend together to create the desired expression by the developer, as a company or as a group of individual human beings. How do the rules of the game effect its dynamics in real-time (or turn-based time)? And how does the "style" of the game add to the mechanics to create the "aesthetics" of the game?
These questions cannot be ignored by game designers - and as these are questions are the foundation of a craft, video games are an artform.