I have the exact same problem as OP and the solutions AndrewT suggested do not work. Nothing in the Steam or Paradox support files work. I have spent three hours now trying to get this game to play but all I can do is get to the launch window, click "PLAY CKII!!!" and then... nothing.
I've tried launching the game via the ck2.exe file and only get this message: "The program can't start because d3dx9_41.dll is missing from your computer. Try reinstalling the program to fix this problem."
I can get to the game launch window if I try to play it through Steam or by using the desktop shortcut, but again: once I click "Play CK2!" from there the window closes and nothing happens.
Note: I have no problem running any other games downloaded from Steam. Just this one. Is this game as super buggy as this forum suggests? Because frankly I'm at the end of my rope here. I can understand needing to do a few work arounds for bugs, etc. to get a game to play but this is ridiculous.