Upon considering the driver side implementation for DirectX API on windows systems for modern video cards I was wondering why this implementation is not available on non-windows
DirectX is a suit of API's:
DirectX components deprecated, but still supported
As you can see many parts of the DirectX suit of API's would need to be rewritten with functionality for Drivers written for Linux. Also some parts of the DirectX suit are likely going to make calls to the Windows OS and that code would have to rewritten for a Linux machine without infringement of the copy-written parts of either DirectX or the Windows OS.
Yes you could write a open source API suit which does the same kind of thing as DirectX for Linux, however without a great knowledge of sound and graphic drivers/support by their manufactures for Linux, it would be a very hard task to do.
However if you question was more of a "Can I get/write something to be able to run games and programs made with DirectX to run on Linux?" in it's meaning, in short no due to more likely copyright infringement.