Being unable to launch Google Earth Pro because it thinks it is already running seems to be happening frequently for me. I am using the Flatpak version if it matters.
Despite killing the application there is still a lock file lingering preventing Google Earth Pro to launch. The error message is specifically:
Google EarthAnother instance of this application is already running.
To launch Google Earth again you need to delete this stale lock file which is inside your user directory:
rm -v $HOME/.var/app/com.google.EarthPro/.googleearth/instance-running-lock
Once gone Google Earth Pro will run again without complaining.