I do enjoy these kind of debates. First thing is first, kick off with a definition. From wikipedia, whose definitions tend to be pretty good:
Art is the product or process of deliberately arranging items (often with symbolic significance) in a way that influences and affects one or more of the senses, emotions, and intellect.
It's a pretty vague definition really, but what constitutes art is a fairly vague subject, so I feel it's pretty appropriate. I think art is something that is made to amuse, move or intellectually stimulate someone. Within that we have works of great literature (Jane Austin, Arthur Conan Doyle, Charles Dickins), great composers (Mozart, Bach, Beethoven) and great painted art (Picasso....yeah). But you also have a lot of commercial, trashy stuff that some pretentious critics wouldn't classify as art because it doesn't meet their artificial standards. I'm talking your American Pies, Transformer movies, Twilight series (both books and films), Harry Potter, most pop music. Maybe even modern art (which is rubbish, but is still art).
Now there's a lot of films, books and tv shows that don't move me in a really profound way. The Liam Neeson film Taken didn't exactly encourage me to reassess my views on humanity (although it did make me reassess my views on film makers). It was hardly Dickensian in it's social commentary. But I'm aware that the makers of the film were arranging items in a manner in which they hoped would elicit some response from my emotions or intellect. Although I suspect the brief for that film was "Liam Neeson beats seven hells out of 27 guards". It is art, just not good art.
The difference with games is that I don't think all games are intended to move you. I don't think the creators of Angry Birds were making a comment on the way the world is (although perhaps they are). If your aim is simply to entertain people, to make them enjoy themselves and nothing more, is it art? I know having fun is as valid an emotion as happiness and sadness, but does that qualify for art, I dunno. I suspect when people say video games aren't art this is their line of reasoning.
But there are certainly, unquestionally games that have moved me and stimulated my intellect as much as any book or film or piece of music. Things like Portal 2, or Monkey Island, or Half Life 2, or Braid, or World of Goo. There are games which make you laugh, even make you cry, and certainly games can do social commentary just as well as any other medium. That is my opinion and ultimately a great many people may disagree with me - but I feel partly that's because there is still a snide stigma to video games that they are not worthy.
When the Beatles came out pop music was in much the same boat, destined never to be compared with the great classical composers. There are still probably people that believe that, but as soon as people started studying the Beatles they gained some sort of validation, and that validation spread to many great pop musicians. I hope that this will be the case with video games, but it really doesn't matter.
I will also say it's really hard to do multiplayer games as art. The point of a multiplayer game is usually the same as a sport or board game - to accrue more points than your opponent. I think there's a few multiplayer games that are really funny or well stylised that might just qualify as art (they are certainly artistic), but FIFA/Madden/NFL will never be art, and neither will Call of Duty either. It's far easier to say things about life (which I reckon is the true definition of art) in a singleplayer game. Hope that helps.
Really good essay and some interesting comments: http://www.popmatters.com/pm/column/146097-why-video-games-might-not-be-art