Well, it's not alive in the strictest sense, because they remove the thing's brain before they slap it onto the plate. They're not monsters. But by the time it hits your table, it was alive so recently that it still flaps its tentacles around and tries to escape when you pour soy sauce over it. What's happening here, besides your own nightmares being harvested and served to you on a platter, is that the octopus' nerves and muscles are still active and spring to life when they come into contact with salt, like the salt in soy sauce.
Evidently, those who partake of this and other types of sannakji say that it's the sensation of the tentacles writhing about inside your mouth that creates the appeal, rather than the fairly bland taste. Because you really know that your seafood is fresh when it's trying to fight its way out of your mouth.
Here, Ock tries to get fresh with this man.