Not currently; the only client right now is a native Android app[1]. However, the server[2] uses vanilla HTTP (for audio) and WebSockets (for data and eventing), so it should be relatively straight forward to build a web frontend.
Even with a web frontend, I'm not clear on how I could get the audio from, say, youtube to go over the websocket instead of to the typical playback device. With something like Pulseaudio, I believe it's possible to stream to a remote host, but then musikcube would need a pulseaudio compatibility layer