HOW? Simple! Just fill out the above form and provide your game key (on GoG, the key begins with "BSGK") or order number (Google Play). If you can't find your Google Play order number, log into your account at payments.google.com and find the Transaction ID for your order.
BUT WHY? Some web features are expensive for us to maintain (like cloud saving), so we can only provide those features to players who have bought the game.