It should not be too hard, the pieces are already there. Extensions already have
a way to stream the tab through
WebRTC (there are probably better examples than that one), so if you use extensions, you do not need to modify the browser itself at all.
You do need a WebRTC compatible client (server?) on the other side in order to accept the stream.
discuss-webrtc might be helpful there, if your searches do not yield anything useful.
For screenshots, extensions have some tab capture API somewhere, look it up in the documentation.