Because if not, this literally fits the definition of "sunk" in the context of a conflict because it's out of commission. Even better because probably there were fewer casualties than a fully sunk ship.

Depends a lot of the ship's construction. They might have a lot of rooms under board that can be sealed individually, so in this picture it might have stopped sinking, and is fine. Then you can re-float it and get the punctures fixed at a drydock somewhere. It would still cost a shitload, supposing the thing isn't totalled, of course, which is the hidden variable here. If it's not sinked, but fixing it is not feasible, then it's as good as sinked, it's only good for scrap.