After installing the game from the current download -
setup_the_witcher_3_wild_hunt_goty_1.31_(a)_(9709).exe
the shortcut points to -
%SystemDrive%\ /gameId=1495134320 /command=launch /path="C:\GOG Games\The Witcher 3 Wild Hunt GOTY"

Double-clicking this shortcut results in opening the C:\ root folder.

I found that the executable is actually at -
C:\GOG Games\The Witcher 3 Wild Hunt GOTY\bin\x64\witcher3.exe

Same same goes for current non-GOTY -
setup_the_witcher_3_wild_hunt_1.31_(a)_(9709).exe

That's a Galaxy command line that appears not to have the proper location for Galaxy. Uninstall and reinstall Galaxy, then uninstall/reinstall the game -- delete that shortcut.

I don't have Galaxy installed.
I don't want Galaxy installed.
It isn't a requirement of the game that I have Galaxy installed.

Then you probably downloaded an installer that requires Galaxy. Go to your account page and check that you have chosen 'More >> Classic Installers' and download again.

Actually the file name setup_the_witcher_3_wild_hunt_1.31_(a)_(9709).exe indicates that this is a classic installer. I have got no idea what went wrong during installation, but you can just create a shortcut to the witcher3.exe file to start the game.