I'm curious if it's using HTML5 or if there's a plugin/extension required to run it. Anyone have ideas on how this works, and if there's any known implementations of it outside of G+?
Currently it uses the Google Talk voice & video browser plugin. If it is not already installed, you will be prompted to install it the first time you use a hangout.
As evidence that this plugin is responsible for screen sharing, if you look at the plugin on your computer you can see that it contains several strings related to screen sharing. (E.g. on a Mac see
in a Terminal.)
Google began the WebRTC project to bring real time communications capabilities directly to the browser, and it is expected that Google will transition chat and hangouts to use WebRTC once it has been standardized. WebRTC is already available as part of development builds of Google Chrome.