The way I understand how Bitcoin wallet addressing works, if you put a static bitcoin address on your game page, you will need to change it (i.e. update the wallet address) every so often due to the problem of bitcoin's block ledger moving forward.
You should instead use something like Mycelium Gear, and upload your gateway page (which Mycelium Gear gives you the code for) to a third-party web hosting solution, and then link to your gateway page from the game page so people can send you bitcoins using a web address that never needs changing instead of going straight to your bitcoin wallet (and maybe hitting an error when the bitcoin wallet URL needs updating).