I think that it can only be art when it can be re-experienced by someone else in the same way as the original. This doesn't pose a problem for a single player, because the way one plays it is fixed. Everyone experiences it in a different way, but they experience the same thing.
Multiplayer doesn't work that way, because the re-enactment by someone else can never be anything like the original experience. You can also see this in game reviews. Whenever someone is reviewing the multiplayer part of a game, or a multiplayer game, they stick to game mechanics, game modes and map layouts. They cannot review it like the single player, which has a replayable experience.
For example:
In a single player game review, the reviewer can point out a particularly nasty section or some boss fight; "When I was walking down the street in level such and such, I got ambushed by a couple of things. It scared the hell out of me"
Now compare it to roughly the equivalent in a multiplayer game: "When I spawned in room such and such, I took a right, picked up the RPG and shot the 12 year old who was screaming in the microphone."
The latter experience cannot be re-enacted, thus it cannot be art. It can never be experienced in the same way. In a single player, one can re-enact the scene in the review. You can also notice this in talking about games with friends. The parts that really spark a conversation are about something you both experienced. You can tell your friend about a multiplayer game you played, but he will never be able to experience it for himself.
Things that can be art, but are not multiplayer:
- A recorded multiplayer game (which is i.e. a short movie)
- Level design in a multiplayer game (which is a static image, like a 3D painting)