My computer does not have a speaker (none built in, and none attached). I watched the clip a few times. Each time, as the button glowed in his video, the button also glowed below the video in the youtube UI.

So, at first I thought that Google is parsing the text of the video being played, but is not listening to your mic.

However, several comments both here and on YT imply that Google is ALSO listening to what you say on your mic. Which, frankly, is much more scary - though I cannot currently test.