One thing that may have relevance here is "game" vs "simulation": The Addy "games" (I don't know if anyone here played them as a kid, basically an education software that rewarded you for completing lessons by unlocking games) had separate sections for games and simulations. Games were pretty straight forward, stuff like Breakout clones and such. The simulations were designed to show the interactions between different variables interactively by letting the user change a variable and see what else happens (e.g. in a forest ecosystem you could adjust the hunting intensity which would then affect the number of predators and prey which in turn affected the health of the forest, etc). They weren't designed to be entertaining but to utilize their interactivity to educate.
Interactive doesn't automatically mean game but at least the cited examples are actually using everything to form their art, many other articles just cite games that look like art (Ico, Rez, Braid, pick your poison) or something, basically a game with art ducktaped to it. IMO it's a case of missing the medium if the art is pretty much separate from the interactive part (e.g. a railroading story that makes the player an actor who has to obey his script should have been a book or movie, not a game). Only by utilizing the interactivity to do things that the other art could not do alone does the game become an art game (or the art become more than just art stapled to a game).
I'm not going to say art games aren't art or aren't games (at least if they have interactivity and a way to amuse yourself with that) but I will say that a game that tries to be art but destroys its game part in the process (this happens mostly through neglect rather than deliberate choice though that also tends to tie into the ducktape issue) is a bad art game.
Of course the example of Graveyard seems to be on the edge, it's hard to say if a software with the only inputs "start" and "exit" counts as interactive (I would say no).
