My solution has continued to work for me since applying it, here's what I did:
You'll find Microsoft Gaming Service folders under C:\Program Files\WindowsApps. The WindowsApps folder is hidden so if you don't see it you'll need to enable hidden items (in file explorer click View>Show>Hidden Items). The 2 folders are:
Microsoft.GamingServices_4.66.2001.0_neutral_~_8wekyb3d8bbwe
Microsoft.GamingServices_4.66.2001.0_x64__8wekyb3d8bbwe
I'm assuming portions of the folder name have to do with versioning so it may not be the exact same name but the key is to find the Microsoft.GamingServices folders.
I then just placed an "x." in front of the name to have the system stop referencing the folders:
x.Microsoft.GamingServices_4.66.2001.0_neutral_~_8wekyb3d8bbwe
x.Microsoft.GamingServices_4.66.2001.0_x64__8wekyb3d8bbwe
What I don't know yet is if these folders will be re-installed after a Windows update.
Here's how you give yourself ownership of the folders if you get an error about not having onwnership:
Right-click>Properties>Security>Advanced
At the top of the Advanced window you'll see an owner listed (likely System), click change and make yourself the owner. In Windows 11 that doesn't appear to be enough to give you ownership and you'll get the error again that you need to give yourself permission to the folder. Go back to Properties>Security>Advanced and check the "Replace all child object permission........" box at the bottom of the window. You should now have full ownership to rename the folder.