@bigmoff
The problem is that the "or higher" refers to higher versions of DirectX 9, not higher versions of DirectX beyond version 9. The game can't actually use the DirectX 10 or DirectX 11 that is installed on windows machines by default nowadays.
The solution is simple; install DirectX 9:
- Download the DirectX Redistributables package from June 2010. Be sure to uncheck any other junk they want to add to it. It should be a file called "directx_Jun2010_redist.exe".
- Run the downloaded file. It'll ask for a folder to unpack in. Make a new folder somewhere on your disk and unpack it there. It doesn't matter where you unpack it; it can be deleted afterwards anyway.
- Go to the folder where you told it to extract.
- Find "DXSETUP.exe", and run that to install the missing components.
- After the installation finished, delete the folder you unpacked everything in.
