This fascinating scene takes place in a restaurant in Hakodate, Japan. The squid is actually dead, but the sodium in the soy sauce causes its muscles to contract. YouTube user richayanami writes:
Dancing squid dishes seem to be at many restaurants in Hakodate, but this particular one may have been the only one with this bowl set. The place was located in the seafood restaurant arcade across the parking lot from Hakodate Station if anyone is interested.[...]
The brain is probably still in the body, but a significant part of its nervous system, the giant axon, I believe extends into the mantle, which has been cut. I'm not an expert on squids so I can't really come to a definite conclusion about that. As you can see in the beginning, it's not moving at all when it's brought out so I assume that signals around the body have stopped, whereas a fresh intact squid out of water would constantly move around.