When you post something on someone's news-feed (etc.) that would be an example of sinking their ship.
Also if you overload a person with notifications you have just "sank their ship".
The cause of this action will lead to LOLing, or LOL circles with your Battleship members.
"Dude when we get home you wanna Sink Battleships?!"
"Let's all just sink Elliot's Battleships when we get home."