Hey RunningOn,
Based on your description, it sounds like you may need to re-run the DirectX redistributable in the GC3 install directory. Please navigate to the following directory:
C:\Program Files (x86)\Steam\SteamApps\common\Galactic Civilizations III\_CommonRedist\DirectX\Jun2010 (Default Steam installation)
Once there, please find DXSETUP.exe, right click and select "Run as Administrator". Once that's complete, please restart your system and try launching GC3 once again.
If you're still having some trouble, I'd like you to place a support ticket so we can gather some additional information from you to subsequently get you up and running. Please see the last section at link below for help with placing a ticket:
https://esupport.stardock.com/index.php?/default_import/Knowledgebase/Article/View/496/161/general-galactic-civilizations-iii-troubleshooting#support
Thanks!