I had the same error. Reinstalling dx, c++ etc didn't help. The following did.
Not sure if I needed all or just some of these, but I downloaded and copied to Fallout 4 install folder these files: * IeShims.dll * mss64.dll * X3DAudio1_7.dll
You can get the DLLs from http://www.dll-files.com/.
Hope it helps, best of luck!