Yes, it is possible to log into Apple Game Center accounts on a computer. However, you will need to use a Mac with the latest version of macOS installed, as well as the latest version of the Apple Game Center app. Once you have these two things, you can follow these steps:
Open the Apple Game Center app on your Mac.
Choose the Sign In option from the main menu.
Enter the Apple ID and password associated with your Game Center account.
Once you are logged in, you will be able to access all of your Game Center account information, including your games and progress.