First a set of examples. If you have the time I recommend the following games
A Company of my-self
Personally, each one of these games say to me that they are art, yet at first I would not be able to give you an easy reason why. Supreme Justice Potter Stewart used the expression "I know it when I see it" when trying to label pornography in a Supreme Court decision, and that is much the same identification that I assume many get when presented with an "art game". Yes, it may be very similar to other flash games, but theirs a "I know it when I play it" feeling one gets from a expertly crafted game.
Discussing this earlier today with one of my advisers, He mentioned that art expresses meaning via a few channels; traditionally either visually or audible. One could say that cooking and possibly sculpture access other senses such as taste, smell, and touch. These games however hit on another level. you receive information via the traditional means (i.e. visual and Audio) but the interaction with the game makes action and consequence part of the "intention" passed from designer to player. For example when one plays "A company of me" you have to lose your companion as part of the design of the level. This mixed with the game's narrative makes an impact into the player as they realize what they are forced to do in order to make progress. And whats more Record tripping shows that narrative is not the only means of "tricking" a player into an experience. I am not a DJ, or have ever tried scratching records but the mechanics of the game create an audio aesthetic that is unique but guided by the design of the game. This interplay between design, aesthetic, and expression is where I feel the definition of "art games" will be found.
What the designer wishes the player to do the player get to do. Since designers rarely seek to design out of their personal cultural expectations, I feel this is how they also act as mirrors of our cultural identity for some time to come. Some design allow choice, others do not but this help us make connections with our everyday life. I believe that this will be true now, and for some time into the future. Hence makes these games, in my opinion, "Art".
When I see posts like the following from the Art History of Games Conference about how games as art maybe a lost cause, I think the speakers may be getting ahead of themselves. Art is not dead, and we need it in our lives more than ever.