Sometimes, the dictionary disappoints. You see the word elephantship and your mind races, your imagination buds and blooms, as you imagine a boat manned entirely by pachyderms. However, the OED defines elephantship as the personality of an elephant. It's the same ship that you find in lordship, hardship, friendship, and governorship, which is not a ship manned by the gubernatorial.
It's also the same ship that you find in worship, which is really worth-ship. There used to be a lot more of these words but they have slowly dwindled and vanished. I shall revive them, though, and set sail on a drunkship to gladship.