Personally, if I were inclined to show off the idea of games as art to someone, I'd go to some of the games in my psn collection. Don't really play 360 but i'm sure there's great examples on there too.
One that a few people have pointed out is flower (i'd put flow too, but think flower takes it's positives and does everything far better) . Just looking at it is you play is a wowing experience, not to mention the score that accompanies it. Navigating with the motion controls makes it feel more free flowing and the whole experience is one that I find calming. It doesn't necessarily evoke an emotional response or have any deeper meaning, but the effect is still profound and beautiful. Of course it's no great feat to play either, you can shove a controller in anyone's hand and let them try it out for themselves. These aren't the only reasons I'd select it though. It helps to break down that simplistic idea that games are all about progression, points scoring and accomplishment. Though you do play through distinct levels and have goals in a way, the lack of any puzzling elements, inherent difficulty or punishment for failure means that progression cannot be viewed as an achievement. I defy anyone to find someone that would proclaim "yes, I managed to beat flower". In order to see games as anything other than competition (either with other players, the game or your own high scores), this example breaks that down entirely, and perhaps potentially leads them open to the suggestions that games can offer something entirely different, for example, offer art
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Not PSN but I'd say the same for the Path, I only played one scenario and found it very haunting. Played the 15 year olds campaign till I found her "wolf" round a mates place. The ending was quite disturbing I must say, but it does offer an experience rather than a challenge. A plus side to using this is that recreations, reimaginings or rerenderings, whichever term suits you best, of things like children's tales and offering them up as allegories for something deeper and darker within human nature or society seems something that critics would view as of artistic merit. The fact that much, in terms of meaning, doesn't seem to be explicitely stated, allowing interpretation to be in the hands of the player (at least that seemed the case in the scenario I played), art often aspires to these goals.
Another I'd look at is echochrome. First is I believe it's actually inspired by one of the worlds the most recognisable artistic images, instantly putting art in the mind of the player. Second is it's unique gameplay mechanic. Making paths and hiding and uncovering holes and jumps, changing camera angles so you fall upwards or jump downwards or whichever way you want. That something so simple carries with it so many options makes it both simple for anyone to try, but layered with complexity you can't help but admire. If that doesn't call forth an argument for games as being of artistic value, it certainly gives credence to the idea that gaming is of higher value than much of it's press gives it credit for.
Final one is linger in the shadows. Okay, even the devs don't consider it a game, but being on a gaming platform, and still involving to some extent (miniscule, but still there) interactivity. Once again because it shakes of the idea of games requiring goals and such. After all, the idea is to progress through a 6 minute clip of bizarre imagary by rewinding time, changing camera angles, and that's really it. You don't even need to do it either, as there is an option to just watch the whole clip as it is. But fiddling with these mechanics adds to the experience. More than anything it eccentuates the point that interactivity can strengthen an experience.
The great thing about these specific examples (i'm sure there's plenty I've missed but you know, can't look at everything) is that they don't rely heavily on things like plot and action in a way that many other literary or artistic forms do, and therefore showcase the individual artistic aspects that are possible only within the medium of gaming.
Of course, underlying this whole thing is a big "why should we care?" Same old thing, if you think games are art, you shouldn't need to justify your claim with such vehemence. With games especially this seems to happen (probably because unlike most other forms, it's universally unregarded as an artistic format, therefore, the minority that do feel their voices need to be heard). The competitive element drew me to gaming in the beginning, as i've seen the possibilities of expanding into new territories, I've wanted to see what other unique experiences gaming can offer. As a general rule, like with everything though, you need to be within the scene in order to explore it, so for the time being at least, videogames aren't going to be viewed as art from non-gamers. But far more optimistic the Ebert meself, I think the more examples the future has to showcase, and the more people that try it out, the more likely it is to be recognised as an artistic medium, and I don't think that point is too far away.