There have been discussions about "games as art" for the past few decades at the very least. Some games - specifically Portal - makes a decent example of a great game that also holds some cultural value.
A new fad for some indie game developers seems to be the abstract/obscure/thought-provoking gameplay direction, however. Skilled post-modern game developer messhof has some of the most interesting games I have seen in years. Not too long ago, a game of his called You Found the Grappling Hook became widely known, and he has very recently released a new game - Randy Balma: Municipal Abortionist (for which the music of the final level is pure chipbliss, in my opinon).
My personal favourite among messhof's game library has to be Flywrench, though. I urge you to play that, now.