Since the game doesn't run in a window and pauses if it loses the focus, I've tried installing it on a virtualized Windows 7 x64 under VirtualBox 4.3.20. Even enabling the experimental 3D options and dxdiag confirming they work, the game just prints "Could not initialize graphics system. Make sure that your video card and driver are compatible with DirectDraw". I found blog posts on AoE2 and AoE2HD which didn't work for this version.

Any tips?

Huh? Where did you get this?
Check my post below how to run it in windowed mode. ;)
http://www.gog.com/forum/star_wars_galactic_battlegrounds_saga/windowed_modecolors_flashingsteam_overlay/post6

Have you already installed the older DirectX9 components within the virtual Win 7? They're missing by default on Win 7.
http://www.microsoft.com/en-us/download/details.aspx?id=8109
Download the file, run it and extract it to a separate folder. Then go there and run DXSETUP.exe to start the installation.
You can delete the extracted files afterwards.

It could also be a resolution issue.Try setting your virtual desktop to one of the games standard resolutions (800x600 / 1024x768 / 1280x1024)