You would need to upgrade the video card to play the game in Windows. D:OS uses DirectX 9c; the EE requires hardware support for DirectX 11.
The Linux requirements have not been announced yet. It is theoretically possible the Linux version could run on your system (when it is released in December), depending on what version of OpenGL is required, and assuming you are willing to dual boot. Given the increased feature set in DirectX 11, though, a corresponding increase in OpenGL requirements wouldn't be surprising.
