Often games come up to a schism when it comes to merging a good story with interactivity, or vice versa. As Yahtzee Croshaw puts it, it's like having gameplay and story locked in seperate rooms and you can only stay in one room, always peeking through the door's keyhole to the other room. That may have been wrong since it was a while since I saw his commentary on Braid, but the point still stands. Games which properly manage to maintain interactivity with a world which involves characters and a plot can be part of games as a storytelling medium. Even stubbornly open-world games like Grand Theft Auto or Just Cause are unable to extinguish the fact that they play out a perfectly lineat story with characters and a plot. They are still linear experiences, they just give the player direction. MMORPGs such as World of Warcraft are even better at this, they give the player freedom to create his own story and the direction offered by the game is often un-noticeable.
One of the criticisms often levelled at World-War 2 shooters is that the story is already there and known to all: the Nazis loose. Innovative attempts to divulge from this version of events usually end up offending a large proportion of people. In fact, games have very rarely dived into that grand lake which I regularly frequent called politick. Some games have subtle nods to politics, but they never venture far from there. Halo's rather blatant religious tones was accepted quite graciously by the christian community and is the one example I know of a quite major game pushing something which was at first glance quite controversial. Storytelling in games is still in it's shaky steps, there are great examples which won't name but it's coming along. Art in games is still a long way off, but a difference needs to be made between labelling games as art and labelling games as a medium. The two are seperate and it does the industry no credit to try and merge them as one under the banner of higher public acceptance of our hobby.
PS: I just found this site after looking up games and art in google.