Using the Desktop launcher from the installer didn't work for me. It would cause a segmentation fault with this error log:

./gog_com-Tower_of_Guns_1.desktop: line 1: [Desktop: command not found
./gog_com-Tower_of_Guns_1.desktop: line 5: of: command not found
./gog_com-Tower_of_Guns_1.desktop: line 6: of: command not found
./gog_com-Tower_of_Guns_1.desktop: line 7: of: command not found
./gog_com-Tower_of_Guns_1.desktop: line 8: Games/Tower: No such file or directory
Running Tower of Guns
Init: BSD Sockets initialized
DevConfig: GConfig::Find has loaded file: ../../Engine/Config\ConsoleVariables.ini
Init: Version: 12097
Init: Epic Internal: 0
Init: Compiled (32-bit): Feb 11 2015 18:27:01
Init: Changelist: 1999891
Init: Command line: -NOVERIFYGC
Init: Base directory: /home/user/GOG Games/Tower of Guns/game/Binaries/Linux/
[0000.05] Log: Sockets: I am AcerLaptop (192.168.178.27:0)
[0000.05] Init: Presizing for 83221 objects not considered by GC, pre-allocating 0 bytes.
[0000.05] Init: Object subsystem initialized
[0000.06] Log: Shader platform (RHI): PC-OpenGL
[0000.07] Log: Textures will NEVER stream out!
Loading library: libPhysXCooking.so
Result of loading library libPhysXCooking.so: 0xb83c500
Loading library: PhysXUpdateLoader.so
ERROR: PhysXUpdateLoader.so: cannot open shared object file: No such file or directory
Result of loading library PhysXUpdateLoader.so: 0x0
Loading library: libPhysXCore.so
Result of loading library libPhysXCore.so: 0xb6df280
[0002.86] Init: Finished loading startup packages in 2.71 seconds
[0002.86] Log: 93911 objects as part of root set at end of initial load.
[0002.86] Log: 0 out of 0 bytes used by permanent object pool.
[0002.86] Log: Initializing Engine...
[0002.88] Init: UEngine initialized
[0002.92] Log: Requested from SDL 2 channels of 0x00008120-formatted audio at 44100 Hz, with 4096 bytes per chunk, received 33056 ears, format 0x00000002 and 44100 Hz
[0002.93] Init: SDLAudioDevice initialized.
[0002.93] Init: Linux client initialized
[0002.93] Log: Supported GL version: (null)
[0002.93] Log: Extensions: (null)
[0002.93] Log: Renderer: (null)
./TowerOfGuns.sh: line 3: 3811 Segmentation fault (core dumped) ./UDKGame-Linux -NOVERIFYGC $@
./gog_com-Tower_of_Guns_1.desktop: line 11: Games/Tower: No such file or directory

Changing the command of the desktop shortcut to start the game directly worked.

Contents of the working desktop shortcut (just change *user* to your username):

[Desktop Entry]
Encoding=UTF-8
Value=1.0
Type=Application
Name=Tower of Guns
GenericName=Tower of Guns
Comment=Tower of Guns
Icon=/home/user/GOG Games/Tower of Guns/support/icon.png
Exec=primusrun "/home/*user*/GOG Games/Tower of Guns/game/TowerOfGuns.sh"
Categories=Game;
Path=/home/*user*/GOG Games/Tower of Guns

Sorry for the long ugly error log, but maybe it can help someone else, when they search for it.