I own Battleship and recently changed platforms. Do I have to buy it again?

To play the game on the new platform, you must buy it again. 

The digital stores in which Battleship is available are separate platforms managed by different companies. As a result, each platform operates independently, and game purchases made on one store do not carry over to the other. This is a policy set by those companies, and as a developer, we have no control over this.