Yes, of course they are.
There. We're done. It's 2015, there's more than enough examples of games with exceptionally beautiful stories, audiovisual components, and mechanics to justify the claim. Anyone who says otherwise is an idiot.
"But games like CoD, Halo, [whatever game here] are dumb shooty things made exclusively to make money!" Furious 7 comes out soon or is out now. It's a movie. Most people would agree movies are art. Billboards and banner ads exist, but we still allow 2D images to be art. The existence of any number of mindless and/or commercial entries into a medium does not dismiss the medium as an artistic one. Bam. Done.
"But art's a single person's vision and blah blah I think having more than one person work or have creative input on something makes it unable to be art!" Too bad it doesn't? I can drive down to the museum and see a whole collection of fine art that's just portraits of rich white people who paid for their faces to be put on canvas. A mountain of the greatest art in the world was commissioned by people who wanted specific things. At least two or three movies that have won Best Picture at the Academy Awards were the product of more than one person's artistic vision. A great director doesn't do all of their own sound design, set design, cinematography etc. They give it to someone they trust will do a good job, and then work with them to make some nice things. (This is a gross oversimplification.) Also there totally are games made by single-person teams. And there are awful movies that are the sole artistic vision of one person.
"But game mechanics are a thing/games can be won/have end-states/have conditional events/are different sometimes!" I'm gonna level with you. This is probably the best argument against games being art. Except it's still garbage, because games aren't film, music, or traditional art. There are more components to the medium. Sure, you can only operate within the rules of the game. If only some creative individual decided that they wanted the player to interact with their world in a certain fashion. Do you know what we call a completely linear, non-interactive experience? A movie. Because that's how they're meant to be viewed. The game's rules are how it's meant to be played. If the player can change the game world then they're supposed to be able to change the game world.
BONUS QUESTION: "What if you miss something because you didn't make a certain choice or look in a certain corner?"
This happens all the time in movies if you don't pay attention. You can miss hints at things. Subtle jokes, foreshadowing, even minor plot points and character names. Sometimes major plot points and character names. If every detail of every piece of art was spoon-fed straight to your face with a giant sign saying "ASLAN IS JESUS AND THIS IS ALLEGORY" then we'd be back to the first point.
"Roger Ebert and Hideo Kojima said video games aren't art!" Someone being famous doesn't make them right. Ebert later kinda changed his mind and, with all due respect, Mr. Kojima is a crazy person. Also Kojima's remark seemed to be referring to AAA games in specific, so... Previous paragraphs. Really this section shouldn't have to be here.
"But you didn't define what art is!" Don't have to, defining something that vague is always a trap. Besides, that shit's subjective.
"But you didn't define what a game is!" See previous answer, sentence one.
Also. Who cares? Video games as a medium don't have to justify a damned thing* to anyone. The medium itself is established enough that it can't fade away short of global electronic failure, a new ET for the 2600, or the heat-death of the universe. I've laughed, cried, and pooped myself more when playing video games. One of those is an exaggeration. All this said, though, stop getting all misty-eyed when some new artsy-fartsy game comes out or when a AAA game has a plot that's actually worth paying attention to. No, they won't change the whole industry for the better overnight because PROFIT doesn't need them to.
*- This doesn't apply in academia where justification is required for funding things. If you need to justify games as art, offer whoever demands justification a couple tickets to the most recent entry in the Fast and the Furious franchise. If the bribery doesn't work, tell them that films are art in spite of those movies, and the tickets were to prove a point. Then go see the movie, because it's probably pretty fun.