Why?

If an web streams video using HTML5 (example: Twitch), when using the Plex for Xbox 360 app, and entering into Twitch channel it is impossible to play the video, the app always returns "there was an error communicating with your plex media server "

Only the PMS log can tell you why. Maybe it is the HLS/AAC issue. Restart PMS, reproduce the error, then check the PMS log and search for MDE to see what decisions PMS makes when you try to play videos from that channel.

Is this the error?
Oct 05, 2015 13:42:23:219 [12768] DEBUG - (Capabilities) Platform ‘Xbox 360’ not matched by plugin platform requirements

@AgomezGZ said:
Is this the error?
Oct 05, 2015 13:42:23:219 [12768] DEBUG - (Capabilities) Platform ‘Xbox 360’ not matched by plugin platform requirements

Yeah I think so. Can you upload the entire log and I will talk to the devs.

Yes! Here it is: pastebin.com/4HA9MmF7