When the payment process completes the game unlocks automatically. You will also get an email with your 'purchase reference' that can be used to unlock the game again in the future should you change machines etc.
Can you run the game (click the 'Greyhound Manager' shortcut from the desktop)? If not the payment process probably didn't complete. Check the payment faq on this forum. Email
support@greyhoundmanager.com and it will be looked into.