I know this is an old thread but I ran into the problem with 0.9.1 and thought I'd share the solution. The problem happens if you have never installed any applications that need DirectX, because of this the DLL that OBS needs is not in the path and so cannot be loaded. This happened to me while building a new streaming PC with Windows 7 which doesn't actually have any games on and therefore no DirectX dlls installed. (I still think this is weird as the OS has support for DirectX).
Anyway to the fix.
Couple of things you can do but the latest DirectX Redistributables are shipped as part of the SDK which you can find here:
https://msdn.microsoft.com/en-us/windows/desktop/bg162891.aspx
There is also an interesting article here if you are that way inclined:
http://blogs.msdn.com/b/chuckw/archive/2012/05/07/hlsl-fxc-and-d3dcompile.aspx
Download them and find the right DLL, latest is d3dcompiler_47.dll (make sure you have the x64 version) and then copy it into the directory where you run OBS MP from.
You could also search around on your machine, I had Visual Studio installed which included the DirectX redist and I copied it from there.
Purely for interests sake as well OBS searches for versions of this DLL to use, it starts at version 49 (d3dcompiler_49.dll) and searches on the path decrementing the version each time until it finds a DLL that it can load. So if you can only find d3dcompiler_46.dll then that will work just fine.
Hope that helps
Adrian