Now the "Ringtail" as far as I can make out, was a sail carried on the after edge (Leach) of a fore and aft sail between the gaff and the boom. This seems more like a light weather sail, similar in principle to the studding-sail (stuns'l) of square rig. Perhaps the drunken skipper had left it too late to hand the ringtail.
The dolphin striker is the thing stiicking down at rightangles to the bowsprit. Presumably the ship in the shanty is pretty well head- down, through carrying too much sail.