It's always very annoying when this happen. I use GOG Galaxy to install my gog games and always install all the files from the game, all the updates, all the patches, all the extras, but always misses one file: the "goggame-[Game.ID.number].ico" (the round gog icon). The backup files have this file and is always installed correctly. Why this file is always missing from the online installation? Another thing missing in the GOG Galaxy launcher, is the option to create a shortcut for the game (with the icon included), just like the Steam launcher. Another strange thing is the Galaxy "Verify/Repair" option, they never detect and repair the missing ico file. So what should I do? Because, to get the 62kb gog ico file and if i have a game with 100Gb or more to install, I will need 300Gb or 400Gb at least. First, for the online installation (100GB); second, to download the backup files (another 100GB); third, installation offline of the backup files (another 200Gb = 100Gb for the temp dir and 100Gb on destination dir), only then I can copy the 62Kb ico file to the first installation directory.
This is why GOG Galaxy is still in beta version.
So the messed up solution that I've got to solve this problem, without having to buy a new Hard Drive, is this:
1 - Download and install PLAYNITE game launcher
2 - Config and synch this launcher with my GOG account
3 - Update Game Library from GOG, and ignore games not recognized
4 - Search and select the game you want the icon
5 - Edit > Download Metadata > Official Store
6 - Select Media label, now you should see the Icon, Background and Cover Image taken from GOG store
7 - Open metadata folder, select and copy the png icon file to the Gog game installation folder
8 - Rename the png ico to "goggame-[ID.number].png", you can do it by copy paste from *.hashdb, *.info or *.script file
9 - In your browser, search for a "png to ico converter" online, drag the png file and download the result ico file to the same directory.
10 - Now you can right click on game shortcut, change icon, and choose the icon on the gog game directory.
I hope this could help many people.