In much the same sense that art exhibits can be art themselves, and a movie exhibiting artful video clips can also be artfully arranged, so can video games be art.
But due to their interactive aspect, games deserve a slightly different attitude. If anybody took a board game or a pen and paper roleplaying game and treated it as art, it would be hard to take them seriously. In fact, the only real "serious" games are the ones that are based on high-strategy and skill, such as chess or sports or card games. There's nothing really "artful" about those, except that the real art is in the game-playing, as it ought to be.
Of course, everyone has a different idea about what a good video game is. And with the industry seeing a major influx of casual-gaming customer base, the power gamers are seeing less and less stuff aimed at them specifically. Casual gaming is quickly becoming kitsch, as power gamers already tend to view it as.