There was an excellent discussion about Braid on this week's GFW Radio podcast (Games For Windows for those not already subscribed to it). There was some talk about "art games", or conceptual games, along with some other examples that are free to play. Getting into the story, they talked a lot about the idea of ambiguity and what counts as a valid vs invalid interpretation of events. It was interesting to note that Jon Blow's favourite movie is Mulholland Drive, though not really surprising.
Hate to go OT, but are arty games really such a new thing on the PC? It seems to me like they've been doing it for a while. Passage and The Marriage aren't as much fun as Braid, but they're definitely arty. Pathologic, though I've never played it, also probably fits into the idea of 'arty' (check here for an excellent deconstruction of it on Rock Paper Shotgun). The IGF usually has a bunch, too.