  Blogger just wrote Babylonia. Anyone know the Species name?  Can laymen extract meat easily? How? I don't know how extract meat! When I last ate this at Japanese restaurant,  I asked restaurant manager to ask chef to extract meat. But manager was dumbfound, and it took five minutes to explain. When the manager came back with the extracted meat, he acted upset.   
Once snails are cooked, they can simply be extracted from the shell with a skewer or a tiny fork. Poke into the flesh, pull if necessary, lift it out. This YouTube video shows it at 3:55 for sea snails (Babylonia areata), the same principle applies for other maritime snails like winkles and land snails, aka the famous escargot. In fine dining, the restaurant would supply a set of special tools for escargot, consisting of small tongs and a narrow fork, to protect the guests fingers from the copious amounts of herb butter classic escargot are served with. In a less refined setting, any kind of skewer will do just fine, even a toothpick. Although I never tried it, I would assume that a set of chopsticks would also work. We can only speculate, but I would assume that the waiter was just surprised that you ordered a dish without knowing the proper technique of eating it - especially as cooked snails can simply be pulled out of the shell without much effort. (Raw snails can be trickier, though, but a well-trained chef will know how to deal with the animals in the kitchen.) 