If anyone's having problems with the launcher not able complete its auto update, Windows Defender might be stopping it (should appear as a notification that Windows Defender is removing the malware).
Sign in to your administrator account
Open up Windows Defender, and go to settings.
Under exclusions, click "Add an exclusion"
Exclude your Ultima PSOBB folder. It's default location after installing it will be in your C: drive.
Now you should be able to use your launcher without being an administrator, but while you're in your admin account, you might as well try using the launcher, then launch the game.