@DrewDad,
Ha!
We went through something similar with the iPod touch, in general (no specific site). Sozlet doesn't have a DS or a Wii or anything, and is over Webkinz and most other web-based stuff (she does really like Physics Games, but not to that addictive MUST DO level). But when we got the iPod (one that the whole family shares), she went through a series of addictions -- Angry Birds, Civ Rev, Doodle Jump, etc.
So I started limiting how much she could use it because I didn't like how she'd come home from school and make a beeline for it. Also she would get so completely engrossed that it caused problems. Like, usually she has a snack when she comes home from school -- when she'd make a beeline she both wouldn't have a snack and wouldn't pay attention to her hunger level until it could no longer be ignored, and then she'd emerge from the iPod after an hour or whatever not only hungry but ABSOLUTELY STARVING TO DEATH, with attendant drama.
Anyway, the limiting worked, and now she still uses it occasionally but the whole thing is much less intense.