What's this shit I just tasted?? GIF

Do you see them moving at all there, where they're tied up and also dead

They're tied up so they don't snip. They can easily move a leg. Crabs are often sold alive.
Another option is the cat just didn't like the taste or licked one of the thorny parts of the shell.

They're red, so they're cooked.. I should hope they're not still alive at this point lmao

Yeah... they are very much dead. And on a serving plate.