I finally solved this world, with a little help from a Steam user. Here is what I posted on the GalCiv3 forums in Steam:
WSS -
Thank you! You go my on the right track, and I suspect I had the same problem as you.
When I attempted to run the program from the GalCiv folderas an Admin, I received an error of 0xc000007b
What I did was download a program called Dependency Walker (http://www.dependencywalker.com/)... making sure to us the x64 version for 64 bit. Once I did that I opened the GalCiv3.exe file using the program.
From there, it listed a bunch of DLL's that GalCiv3 was referencing which I didn't have on my computer. Additionally and most importantly, it was referencing a DirectX11 DLL (maybe the same one you found) called 'dsdx11_43.dll'. I had this DLL on my computer, but it was versioned for 32 bit, rather than 64 bit.
What I did was systematically go through and added the missing DLLs and updated the 32 bit one to 64 bit by downloading each of them from: http://www.dll-files.com/
Once the DLL was downloaded, i copy/pasted it into the c:\Windows\System32 and c:\Windows\SysWOW64 folders. You must have admin access to do this, I don't take responsibility if one of you tries this and messes up your computer. Back your stuff up!
Linked below is a screenshot of the what the DLL looked like in the sys viewer. Notice how the highlighted DLL is listed as x86 under the CPU, not x64 like the rest
https://goo.gl/Y2w4gG
Once I made those corrections, the game booted right up!
