For now you can't add a media stream from a video tag, but it should be possible in the future, as it is explained on MDN
MediaStream objects have a single input and a single output. A MediaStream object generated by getUserMedia() is called local, and has as its source input one of the user's cameras or microphones. A non-local MediaStream may be representing to a media element, like or , a stream originating over the network, and obtained via the WebRTC PeerConnection API, or a stream created using the Web Audio API MediaStreamAudioSourceNode.
But you can use Media Source Extensions API to do what yo want : you have to put the local file into a stream and append in in a MediaSource object. You can learn more about MSE here : http://www.w3.org/TR/media-source/
And you can find a demo and source of the method above here