I work in the online learning industry, mainly with higher education institutions. One of the top features required by instructors is the ability to provide audio feedback to students. And this is really a huge benefit for them because most instructors are not fast typists and they have hundreds of assignments to review every once in a while.

Faster than typing would be great. What's not so great (or so fast) is trying 3 or 4 times by voice and having to go type it anyway because the accuracy's not there. Sooo, like my old-aged ancient geriatric friend in the parent, I too still preferentially go to the keyboard, since I figure I'll probably end up there anyway. If it's a social situation I usually preface the typing with some variation of "All right let's see here..." which sounds like I'm trying to figure out something hard or ask something of the Great Oracle, but really it just means "I'm about to type."

Maybe once speech recognition advances a bit more...

But it's only for searching after you've already navigated to a search engine, right? You'd have to be extremely slow at peck-and-hunting for it to save you much time (especially as search strings are so short) - and in the video you have to click "submit" to even do the search (and then presumably navigate normally with mouse). I can't see many instances where this could be worth it. Maybe I'm actually too young to see why it's useful!

Maybe the search engine is your homepage, or you just have to hit "g" and enter to get there, or it's bookmarked. Maybe you don't have hands, but you have an easy way to move a mouse around and click. Maybe you're eating a sandwich with one hand and don't feel like putting it down. Maybe you won't use it for a short query like "weather", but you will for sentence-long queries. Maybe you want to search "linux won't recognize wireless keyboard".

It's very easy to think of instances where this will be helpful.