DirectX 9.0c was a standard for many games, and when Windows 8 came out, it "wasn't there" by default, because the newest version of DirectX had been released (Direct X11). Theoretically, DirectX's are supposed to be backwards compatible--as with most programs that are upgradable, like internet browsers--however the release that came with Windows 8 "forgot" that some older DirectX 9 programs called specific DLL filenames to check for, and in order to run.
With Windows 10's release, I've noticed they've managed to "fix" that issue to some degree. It's far more backwards compatible with DirectX 9 games. In fact, I ran Togainu no Chi and DMMd perfectly fine without finding the DirectX 9.0c runtimes.
In short, make sure your DirectX is up-to-date, and it should take care of the issues for you. ^^