What are the Screensharing in Messages requirements?
According to Apple those are the requirements for audio and video chats and screen sharing.


Camera (video chatting)
Microphone (audio and video chatting)
Internet connection speed (upstream and downstream)


  Share your screen or share a friend’s screen:  128 Kbps

Mac OS X version of people you message
Computer processor type of people you message


Source: Messages (Mountain Lion): Requirements for audio chats, video chats, and screen sharing