I'm attempting to play this on Windows 10.

When I launch it from the Galaxy app I don't get a game window but I do see the game application listed in the Task Manager under Background processes. I have to force the task to end to get it to close.

I can launch the game outside of the app. When I do, I get a UAC prompt because the games installs with Run as Admin checked. The game seems to run just fine after that.

Any ideas why I can't get the game to launch from the Galaxy app itself?

Probably because Galaxy is aimed at a useless start script instead of the actual game.