There are no gyrations. It is just a joke based on reality. I am a Louisianan living in the North. People sometimes make jokes to me about eating alligators, squirrels and even road kill. My response is to say “Oh, hell yeah!” (especially to the alligator). It is awesome and I am not happy that I can’t get it easily anymore. It is no more racist than saying that people in Maine eat moose because many of them do.
You are letting your own bias show. There is nothing inherently wrong with eating a deer versus a cat. It is just the former is perfectly acceptable in U.S. culture while the latter is not.
Double-dog pro-tip (no pun intended) - people don’t literally think that Asian people in the U.S. serve Fido and Fluffy in mainstream Chinese restaurants. It is just a cultural joke that isn’t meant to be taken seriously.