-Post contains spoilers!-
Of course video games are art. I don't see how they could be seen as otherwise.
Don't video games tell stories? Do their characters have personalities, feelings, thoughts, and resolves?
Don't they have worlds, settings, and creative use of devices used in cinema and writing, such as motifs?
Of course video games are art. Metal Gear Solid's Snake is an exceptionally deep character who, if you followed the series from start to finish, you can become attached to.
Art is, by definition, something that invokes emotion. I felt concern for Snake who was going through a horrible case of accelerated aging and deteriorating health through MGS4.
I could understand how Big Boss felt at the end of MGS3 when saluting The Boss's grave.
I could understand Luke Fon Fabre's guilt in Tales of the Abyss when he had to fight the real Luke to see which would survive.
The stories of video games generally pique my interest, and many have an impact on me, just the same as an intriguing painting, emotional movie, or engaging video would.
Video games have unlimited hours of time to tell their stories as well, giving you much more time to get to know the characters that they contain, much like books.
If you thought Indigo Prophecy's story was cut short, it'd be a lot shorter and have much less to tell if it were a movie. Also, speaking of Indigo Prophecy, that was another game that was actually meant to make its players feel concern for the characters lives throughout its content.
The much shorter time per movies is also why video game to movie conversions usually art terrible.
The interactivity of video games is actually a very nice device to create a deeper impression on its audience.
MGS3's ending had a nice example of this. The Boss had to be put out of her misery after being defeated by Naked Snake. Instead of having him shoot her one last time in a cutscene, it gave the last shot to the participant instead.
I've also heard the argument that video games can't be art because they're interactive, but it isn't hard to see how this is incorrect.
http://en.wikipedia.org/wiki/Interactive_art
Already shows that interactive art is legitimate.
If anyone is still unconvinced, then there's also the fact that if you automatically exclude video games as art just because they are interactive, you're also excluding this very impressive piece of art:
http://www.youtube.com/watch?v=BZysu9QcceM
Another very strange argument I've heard is that video games can't be art because they're a combination of different arts, which means movies, television programs, youtube videos, and stage plays can't be art.
What Video Games, books, movies, television, traditional, and all other forms or art have in common is that they were created with a vision in mind with varying detail in mind on how they will impact their audience.
Because of this, I simply cannot understand how exactly video games can't be thought of as art.