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Why is the linux version of the game delivered as an tar-archive and not as an sh script? How do I make a desktop icon and integrate it into gnome applications menu?
This question / problem has been solved by darktjmimage
I can't answer why gog decided to make it a tarball.

To create a menu/desktop item, the easiest is to just copy from another game. For example:

cat >gog_com-Observer_1.desktop <<EOF
[Desktop Entry]
Encoding=UTF-8
Value=1.0
Type=Application
Name=>Observer_
GenericName=>Observer_
Comment=>Observer_
Icon=/path/to/gog_observer/support/icon.png
Exec=/path/to/gog_observer/start.sh
Categories=Game;
Path=/path/to/gog_observer
EOF

Replace /path/to/gog_observer with the full path to the untarred gog_observer directory. If the path has spaces, you will probably have to put the Exec= argument in quotes.

Place the resulting file in ~/.local/share/applications for a menu entry and ~/Desktop for a desktop icon.

Then, file an issue with gog support asking them to replace the tarball with an installer. I won't do that, because I don't care, and I have deeper issues with this game (i.e., it doesn't work at all on my system, but it will be some months before I get around to trying to fix it again).