The "Unable to initialize DirectX' error message is often related to an outdated/corrupt installation of DirectX. Could you try removing DirectX from your system completely, and reinstalling from scratch using the package linked above?
Were there any issues at all during installation of the game? On some machines the .NET framework takes a long time to install and seems to hang, if this is the case for you and you suspect that it may not have installed properly, you could try downloading the full .NET Installer
from Microsoft. Scroll down on that page until you see a link called ".NET Framework 3.5 Service Pack 1 (Full Package)". Unfortunately, it's quite a large download.
While I think this is unlikely to be a solution, you can try the Latest Prerelease
version of the game. To update your game to the latest prerelease version, extract the zip archive on the linked page into your AI War directory.
As suggested by liq3, there have been reports that AI War does not interact well with software such as mumble, have you tried quitting all other running programs to see if any of them are interfering with the game?
Thank you for attaching your error log. Could you please tell me which version of Windows you're running, and which graphics card you have installed?
I'll continue to assist you as well as I can, though if we're unable to find a resolution at this stage I assure you that the developer will be available to address this issue no later than Monday.