EndlessKnight: As far as I am aware, the Galaxy client was not installed
Lenkorn: I am also unable to launch this game via the Galaxy client if it is offline
nightcraw1er.488: Thank you both, I will add this to the list of enforced client install games then. Makes me sad to see this happening.
To EndlessKnight, I'd just like to note that the GOG Launcher seems to be an early version of the Galaxy client, as it installs to %ProgramFiles(x86)%\GalaxyClient.
More importantly, I'd like to point out that the Double Dragon Trilogy installs two Start Menu/Start Screen shortcuts. The first is in the "Double Dragon Trilogy [GOG.com]" subfolder and has a red background. It, like the identical Desktop shortcut, launches through the GOG.com Launcher. A second shortcut is in the general "Games" subfolder and has a blue background. It launches the game directly, without the launcher, and will never bother you about failed log ins to Galaxy (which sometimes happens at various menus if you open the game through the launcher while offline).