David
I have looked at the video a few times. I have a feeling that the edits are carried out on perhaps ten or so groups or vertices/faces with each group having two or three edits that can be applied
So it comes down to ascertaining which region or group the user seems interested in/has click on. Show the puff of smoke to indicate which region you think the user wants to edit. Then use the mouse up and down and side to side movement numbers to the stretching or whatever is the designated behavior for the group.
The model you attached is built with Three.js. You should be able to select groups of vertices using a Three.js Ray. Mr.doob and Lee Stemkoski both provide examples on using the Ray.
Even having said all that, please note that this is a WebGL mailing list and not a Three.js list.
And, nonetheless, I would be delighted to see what Jack could put together in actual WebGL ray-casting.
Theo