Yeah, having DX11 installed is not the same as your hardware actually having the required features to use it, unfortunately. The only way you will currently be able to use OBS is to get a better computer.
Expanding a bit upon what paibox said:
Streaming is incredibly system intensive. Even top end hardware is pushed to the limit streaming and playing games at the same time. After the rewrite, which should support older hardware, you are still going to run into the performance limits of your older hardware. So, even if it works, it's really not going to work WELL.