Yes...it's rather easy if using one of the game launchers like Steam, UbiSoft, GOG, etc. as they have a setting to change the game installation folder location.
Games not managed through the launcher usually have an option in the install procedure to direct to another folder location too.
It's not an issue with the processor at all. Any OS is designed to do this and has been since DOS.
It's more difficult to move an already installed game though. It's usually easier to uninstall the game, change the installation folder location in settings, then reinstall it. But you have to go through the whole download process again.
You can move the files if you find them, then tell the launcher to search for them and then validate them. That's usually faster.