I would have suggested American McGee's Alice (female protagonist), but it's fairly violent, though it has a fantasy landscape & timeless cartoony appeal that's deffinately artsy.
Get her this PC game called "Aveyond," it will cost you all of $7, & if she likes it, there's a whole series of them. It's kinda like the classic 2D Zelda & Final Fantasy games. You can buy it at Amaranth Games or BigFish games.
There's always "The Sims."
There's also this VERY artsy game called "The Path," a goth version of Little Red Riding Hood. I don;t know if it's violent, but it's grim. I think it was a $10 downloadable.
Speaking of grim, there's "American McGee's Grimm" & other episodic game series like "Sam & Max," "SBCG4AP," "Wallace & Gromitt," & "Tales of Monkey Island." They're all funny, unviolent, & very artsy. You can get these at GameTap or TellTale Games. Just buy her an episode, if she likes it, she can buy the rest herself.
Another artsy game girls like is the "Nights into Dreams" games.
& lastly, "Silent Hill."