Food

No, it is a *cephalopod mollusc* (Octopoda - "Eight legs"). Not all Cephalopoda have shell, nor can they be called Shellfish.
Octupus is a mollusk.

Not disputing the fact that it's a mollusc as Cephalopoda are a class of the phylum mollusca . Correct, very few Cephalopoda have shells ( nautilus being one obvious exception) but this doesn't mean they can't be blanketed under the term "shellfish" in the culinary world ( this is the food thread after all). If you were to apply your logic here then surely shellfish would literally mean fish with a shell which of course would rule out everything we currently class as shellfish ( prawns, crab, oysters ).

I think "shellfish" is a very loose term though and this is just my opinion.