gamecenter.exe is part of a product called known as GameCenter Application and the developer is http://joyvy.com/ .
If you think that this file contains a virus or another malware, please download a virus scanner.
If gamecenter.exe is using too much CPU or too much memory in your system, it is possible that your file has been infected with a virus. Installing an antivirus is recommended.
Not all processes can be uninstalled without the help of a 3rd party tool, especially malware. To see if it can be uninstalled, first go to Start > Control Panel > Add/Remove programs and select GameCenter Application from the list to remove the process gamecenter.exe from your computer.
If you have any problems with gamecenter.exe, you may try using a registry cleaner or a speed-up software to check, analyze, and fix problems that are affecting the performance of your computer.
You may try contacting http://joyvy.com/, the developer of gamecenter.exe and ask for more information.