DirectX is software used by Windows and is currently up to version 11, but DX11 only works with Windows Vista and Windows 7.
You also need a graphics card with the proper hardware DX support. If your graphics card does not support DX8.1, then it does not even matter if you have DX9, 10 or 11 installed on your PC. Without the proper DX support on the graphics card you will not be able to play the game.
In short... you need a newer graphics card.