The site has been updated with the first of its social games, called King Under the Mountain. It's a "tactical strategy game," and the schtick is that it's derived from a game played by the dwarf lords of Khazad-Dûm. It involves very Dwarven things like "caverns, gems, and fighting." You can play it alone or against your friends, and it's pretty cool.
Actually, we're just assuming the "pretty cool" part because unfortunately before we could check it out for ourselves, the site was shut down for maintenance. Apparently it was hosed "due to overwhelming response" from interested LotRO players. It'll be back up at some point though, if it's not already by the time you read this, so keep checking back if you're interested.
[EDIT: Site's back up. Enjoy!]