CEP is built on top of perticular version of chromium project.
e.g. CEP7 runtime has been built on top of Chromium version 41.0.2272.104. Chrome provides updates very frequently but it takes time for CEP to adopt to the chromium version. They release new CEP version based on chromium version .
So it is very clear that, all chrome capabilities are not available in CEP.
I am not aware of Web Midi API, is part of Chromium version 41.0.2272.104 or not. Please check accordingly.
Thanks,
Dnyanesh