It seems that the feature has either been removed from the settings at some point (either accidentally, or for a reason), or was planned but not yet added.
Currently you can choose to create a shortcut the moment you install the game, like in the following screenshot:
If you've already installed the game and missed the opportunity to create a desktop shortcut, fret not: GOG will have automatically created a shortcut in your Start Menu.
Since GOG, unlike Steam, doesn't put shortcuts in a shared Start Menu folder, you'll have to search for it. Simply open the Start Menu and start typing the name of your game, for instance Dark Souls
if you want a shortcut to your death.
From here, copying the shortcut to your desktop shouldn't be much more difficult than beating Zelda 2, though different OS and OS versions will require different methods.
- Windows 7: Simply right-click -> copy, then paste anywhere you like.
- Windows 8, 8.1, 10: Right-click ->
Open file location
. This will open a File Explorer window to where the shortcut is located. From there, just copy and paste the shortcut wherever you wish.
All that's left to do now is hope GOG will eventually give us an easier way to create shortcuts. In the meantime... did you go to the toilet before visiting Tartarus?
Best Answer
The GoG team have marked the "Auto update galaxy client" wish as completed. The wish-list can be found at here. This strongly implies that it does indeed have the ability to auto update itself.