
For no good reason I'm going to split games into groups which I'll half-heartedly analyse for artistic merit! Thankfully most games fit into a very small group of niche categories.
Shooting. These appeal predominantly to guys and every so often an occasional girl (who wants to be a guy, no doubt). Age is irrelevant as I've seen all groups from eight years old up to 70 years old get involved in some old fashioned virtual gun play. There's very little scope for a game that's based on the concept of pointing a shooty thing at someone/thing and then killing them/it, to be artistic in itself. Some games do use art as a way of making themselves stand out from the crowd. Recently Madworld on the Wii could be considered "artistically striking", and in common terms that would be enough to label it "art". In fact, for me it is enough. I used to consider myself an artist and did all the studies and work involved in becoming one, yet most pieces that people currently call Art, I call crap. There are many games that have more feelings in their depictions of characters, better technical skills in anatomy and expression, are more thought provoking and excel in every other individual component that can be used to define art. Actually, I say "many" games... Really I mean "some". When I say some, really I mean "a few". In fact, when I say a few, I mean "a couple". The point is though, that they do exist!

Football Management. No, actually I'm joking... The most artistic thing related to these games is which font they use to display the database. Excell spreadsheets are not art, as far as I'm aware, neither is Football Manager... Unless you're some kind of astounding moron of course!
MMO's and RPG's. These have a massive amount of (in my opinion, generic) Art used in them. Both in the creative process and in the final product. I'm not a fan by any stretch, but I absolutely concede that Fantasy and Sci-Fi art is a massive percentage of the worlds complete paper based artwork. So even if there are about six hundred million variations on a lady Elf with big cleavage, and then about the same amount of large helmeted warriors, it's still classified en masse as art...
Other Genres. I can't really be bothered going into more than this currently... Maybe some day I'll add to this and start listing micro-genres aswell, such as "Native Indian Axe Throwing Simulators", but for now I'll stick with what I've got!

This process is similar to the Sistine Chapel. One overall end result, or piece of art, comprised of many separate and smaller pieces of art. The Chapel was of course painted by many more people than just Michelangelo; there was a whole team of artisans working on it under his instruction (much like game developers working under a project leader). Consider also that the chapel is made up of many smaller "works of art" that combine to form the complete "masterpiece". As I previously mentioned, games are made up of lots of little pieces of art also. In many cases lots of pretty rubbish pieces of art, but still the analogy is there...
Where the disagreement really stands is in the perception of what Art is. We live surrounded by various forms of art, in buildings, furniture and occasionally even fashion, though maybe not so much here in Scotland... Our TV's broadcast Art at us occasionally, we read it in books, we rent and watch it sometimes and we even view it in (very VERY rare) adverts. Most things that have a creative process involved in making them can be termed art by certain people, so maybe the problem is really that I've not been talking to the right people? There are undoubtedly many people who consider games artistic, yet I have a fondness for the media and want to see it accepted by more than just it's existing fan base as something truly creative, so I prefer to debate it with heathens, I mean "non-believers"...
On top of the points already made, the single biggest factor that weighs in on this argument are the waves of "indie" games that are starting to take a bigger and bigger slice of the games market. Some are truly bizarre, ugly, poorly executed and can even be in very bad taste, yet there are others that are so captivating because of the artistry involved in them that there can be no debate at all as to whether they're art or not once they've been experienced. I've no real notion to tell you what games in particular I'd classify as Art, as that's down to each of you and your own opinions... I'd suggest that you go and look further into the matter for yourselves though!
Actually, let me suggest one single title that's both indie in it's enthusiasm and freshness, but also mainstream-ish... Beautiful Katamari. Just. Rolling. Awesome. Ness.
You should go and google the Museum of Bad Art. Genius in a bottle... (paint remover).