Don't worry, that doesn't mean your account has been compromised :)
This error message means that GOG Galaxy is already running on another account on your Mac.
Rebooting your Mac should make it go away.
Also you can try to shutdown all GOG Galaxy process:
> Press Command + Spacebar to open search bar.
> Type Activity Monitor and open it
> In new window find Galaxy, click on it and just click "Quit Process"
Now you should be able to launch Galaxy Client without problem.