WebRTC is normally used in bidirectional use cases like video chat with text options, so I don't think it so odd that VLC doesn't outright support it. VLC does not support dialing into an Asterisk server, either.
Maybe I'm wrong but in this case, couldn't you create your own middleware server that could consume the Weber stream feed and then stream out as a regular vlc consumable feed? I'm guessing there will be some transcoding on the fly but that should be trivial..