Indeed, Firefox supports the standardized Media Source Extensions, but you also need to confirm that the content you are trying to play is supported in terms of video and audio codecs.
You can find the supported codecs for Firefox here. So, the key for cross-browser compatibility is to use the audio and video codecs supported by all browsers.
Also, there is a much newer version of the DASH.js player currently available, perhaps you want to give it a try: DASH.js 1.1.2