I'm not sure if it actually works this way, but it seems to me that art starts as amature experimentation, develops when it becomes lucrative and is funded, and only becomes fully explored when amature experimentation can be done at a level that's close to what is being done by funded artists.
This has certainly been the case with art media in the past (dammit I'm still not talking about actual games...) with writing, painting, photography, music and movies.
Writing is easy. When the masses can get their hands on pens and paper, you get literature. Painting was, for quite some time, something done for royalty and aristocracy. Mass production and the breakdown of feudal social networks allowed for painting to progress beyond establish styles. At this point whoever wants to paint can paint. Period. Same with photography. The Kodak hand camera was downright feared by professional photographers of the turn of the century. They thought it would ruin photography as an art and make it crude. They didn't know that some of the greatest stylistic breakthroughs would come from a six year old.
Anyway, the trend is partway finished with video games. Tetris and Pong were created by programmers as playful experiments and theoretical tests. But games are hard to produce and few people have the expertise to make one from scratch. In fact, the barriers preventing just anyone from creating a game have been so massive that video games have been an entirely business oriented art for just about its entire history. Only recently have we finally found a method of producing video games without the need to be funded.
Flash and other internet animation programs are allowing people with relatively minimal programing knowledge to experiment with appearances and game formats and make games in their spare time.
That being said, I'm pretty sure not much real experimentation has happened yet. Many of the best flash games are still only experimenting with visual styles and simple game layouts. There are still very few games that are actually trying to make some statement using the gaming structure.
However, I do think this is a way really good games can and will be made. It takes someone with nothing to lose to make soemthing that's never been attempted before.
The alternative is for some decently large companies to put their necks on line. I'm sure many would claim that this is already being done, but in actuality I think very few companies have really put themselves out on a limb for the sake of making a really artistic game. Though some of my very favorite games could be considered the result of just that.
The new online formats that the major platform systems include are facilitating this sort of avant-garde game exploration. Flow, one of the most beautiful, albeit simple, online games I've come across has been picked up by Sony and has been ported to the PS3 as a downloadable game.
I'm honestly not very sure how seriously independent game designers are taken by the game industry, but there are some really great things being made. I'm hoping that as people experiment with creating games fans will begin to expect different things and turn to each other for their games the same way we've done with video and music entertainment. When that happens, maybe people with money will perk up and fund some amazing ideas.