Usually full versions of the games are recognized automatically right after the purchase but, unfortunately, sometimes errors occur and the system cannot recognize certain purchases.  

If you are still asked to purchase the game after re-installation, please, tap the 'Buy Now' button in the game and continue the process. iTunes allows to re-install purchased apps for free and in this case, you should not be charged anything. 

If the problem still exists, please, submit a request to our Support Team and we will respond to you shortly.