I don't think I've ever seen one of those in LA. There are definitely some unique and fun restaurants though:
AFloat Sushi - where they send the sushi past you on little boats and you choose what you want.
Melting Pot - a chain with several locations in LA. All fondue.
Empress - I believe that's the right name (it's the most popular dim sum restaurant in Chinatown and they serve very traditional dim sum dishes)
By Brazil - traditional Brazilian BBQ located in the Brazilian area of downtown Torrance. Buffet style except for the meat which they come around and shave off huge spits onto your plate.
Roscoe's Chicken and Waffles - fun place, great food, and yes, fried chicken and waffles served together
Neptune's Net - on PCH in Malibu, you pick the seafood from a tank and they cook it for you right there. This restaurant was featured in lots of moives.
Inn of the Seventh Rey - you sit outside next to a brook and deer and other animals come right up to your table. All organic and natural food. Very romantic.
Hope that helps.