Not just the economic aspect, but the game aspect. Board games and role-playing games have been around much longer, and aren't considered art (and there doesn't seem to be any push for them to be considered as such).
I could definitely seem board games as art. As for RPGs, the books themselves are art as are the stories produced. A given session of play would also be art; akin to some kind of improv/acting, though not done with any thought given to an outside viewer. As for the system of rules... that one I'm left unsure of but it may be art in a same way some see elegant code as art.
[EDIT] Why is my parent being downvoted? It is a legitimate question, and we should try to answer it.
Yet there are a lot of board and roleplaying games pushing their boundaries regarding theme and mechanics:
You have boardgames exploring difficult themes (Train[0]) and others being defined as they are played (Fluxx[1])
On RPGs, You can have rpgs about simple themes as being a housecat (Cat RPG[2]) or serious one like rape and domestic violence[3]. In terms of mechanics, there is Dread[4], a horror game that uses a Jenga tower instead of dice.
There is no push to be considered art, but there are folks doing some really cool stuff with the medium.
What is happenning with videogames is that there are people who thing "videogames should grow up" and "stop playing around". That, in my opinion, is stupid. You don't tell a 15 years kid to "grow up". It will come out naturally. KLEt games mature on their own.
Actually, Train was the first thing that came to my mind when typing that comment. The fact that we both immediately thought of the same niche game that apparently has only been played twice without it's creator present suggests that these things aren't terribly common (that's not to say that these edge cases aren't interesting). But maybe a die hard board gamer can correct me, since there tends to be a lot of interesting stuff that goes unnoticed (this is definitely true for video games, I'd be surprised if it wasn't true for other games).
The people who seem to be pushing for games to grow up or talking about Citizen Kane moments (and seemingly forgetting about silent films) seem more interested in validation than anything else. There have been interesting games for decades; if they're truly interested in these, all they have to do is play them.
As for videogames, the language of the creators themselves sometimes seems to acknowledge the relation to narrative and cinema. Some game designers style themselves "directors", and are sometimes more interested in cutscenes and "telling a story" than in actual interactive gameplay. Note I'm not telling whether I think this is a good or a bad thing :)
I think some of it goes back to the art vs. design conversation and games, in so much as they are games, tend to fall on the design side (there tends to be a clarity regarding the rules, rules are designed to create good gameplay rather than an expression of artistic vision, etc.). A lot of the things that can be considered art can work just as well outside of the game (take a cutscene, for example, which has no gameplay and is basically a movie inserted into a game).
Of course, there are some games that tie the narrative and the gameplay together in such a way that it's hard to separate the two, such as The Colonel's Bequest (1989), The Last Express (1997), and a favorite of Roger Ebert's, Cosmology of Kyoto (1994). There are also "ungames" that eschewed gameplay in order to create more of an art experience, such as Puppet Motel (1995) and The Manhole (1988). But mainstream gaming has largely forgotten these games (as well as many others).
Good examples! I regret that mainstream gaming has forgotten these games. Non-mainstream gaming hasn't, fortunately. There is the Interactive Fiction community, which has produced some of the best games I've ever enjoyed; there are some indie designers doing experimental games about personal issues -- I'll avoid mentioning them, because that's a can of worms I don't want to open here -- there is the "agitprop" of Molleindustria's Paolo Pedercini, etc.