Vamrem: There is a solution for Steam, making Steam launcher create a shortcut to desktop, and then, replacing it in my Start Menu.
But I can't find that function in GOG launcher.
When you install a game there is a checkbox for making a shortcut on the desktop. There is also a setting, click the GOG icon -> settings.
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However, you can manually modify your shortcuts, by clicking properties. Here is an example:
Target - "C:\Program Files (x86)\GOG Galaxy\GalaxyClient.exe" /command=runGame /gameId=2067763543 /path="D:\GOG Games\Kingdoms and Castles"
Start In - "C:\Program Files (x86)\GOG Galaxy"
Change the gameId to the id of the game. You can find that info using the GOGdb, make sure the "type" is game and copy the product id:
https://www.gogdb.org/
Change the path to the path where your game is installed. This will tell the shortcut to launch Galaxy (if it's not already open) and run the game through Galaxy before starting.
EDIT: This is of course assuming you are on Windows.