Well-executed, inspiring games are, to me, art in every sense of the word. I'll give a few of my examples:
Okami -- This game is, first and foremost, beautiful. It also lays claim to a storyline that follows a few very interesting and immersive Japanese myths, and the gameplay just adds to the art and the style of the game. It was very well done and I can play it for hours, just enjoying the look and feel of the game.
Final Fantasy X -- If nothing else, the story of this game makes it art. The world that is created and the characters that pull the story along make this game an easy example for me. It brought me to tears several times, and just thinking of it brings back much nostalgia.
Mass Effect -- In this game, the art is the aspect of choice. So far, I have seen no other game that accurately portrays cause and effect, or the simple action of consequence so well. Every decision you make affects the world and people around you, making this game an art in the immersion that is felt from making choices that affect everything and anything.
However, these are just examples of games that feel like art to ME. Any game can be perceived as art. As blipblop said, it's all in the eye of the beholder. True art is something that makes you feel something beyond what is apparently seen... and this can be different for everyone. To one person, a black smear on the wall is something to clean up. To another, it could be a masterpiece worth sharing to the world. Art is a difficult thing to truly define.
In short, I think anything can be considered art, and that includes video games. I know that certain ones have truly altered my life and my perception... and so they are art to ME. It honestly just depends.