Does anyone know how much effort is required to produce this sort of video, perhaps from a script?

I have a friend who has been doing video editing and compositing for over a decade -- I'm currently talking with him about this.

As for myself, I had a project similar to this one -- a pop-sci movie about geothermal energy in TV resolution that had to be done in a week, plus it had to look professional (it was intended for a top European official). Long story short, we did it (we handed down the copy to the courier about an hour before his plane departed). Here are some useful tricks I learned from that project:

The easiest way to go is to make it text-driven -- i.e. the text is master, the video is slave. You get the text first, break it into episodes and come up with video fragments / screens to illustrate each text episode.
Finalize the 'script' as early as possible. We used an MS Word table with three columns: Text (literal voiceover text), Timing and Video (a description of what's going on on the screen). Each row represented a single screen / episode. In the absence of the actual voiceover narrated by the final voice actor, you can measure the approximate time of each episode by mentally speaking its text and using a stopwatch (we used an old-fashioned analog one, worked great). When a timed script is ready, you can parallelize the voice recording and the video work. Also, since LessWrong Wiki supports tables, such video scripts can be authored and edited publicly.
Final script is final. Don't edit the script after it has been finalized and sent to production. In our case, the text author attempted to tweak it after we've timed it, but we refused -- we had a good reason, one-week deadline.
Use a professional voice actor. Since we went with the text-driven approach, this was very important. We hired the leading actor of our local dramatic theater, and the result was great. Actually, it was almost magic -- basically, we just stitched together a bunch of unrelated videos, added a voice, and somehow got a TV-grade product.
Stock images, vectors and footage are your friend. When I worked on that project, there were no such things, so we had to dedicate a guy to video scouring. These days, quality images, sounds, vectors and footage are dirt-cheap, and there are literally millions of them available.
Localizations: same sentences translated to and spoken in different languages have different duration, so additional time is needed to adjust a localized voiceover to the video. In our project, the Italian voiceover turned out to be ~15% longer than the Russian one, so I had to compress some fragments of it to squeeze it into the video timing (re-adjusting and re-encoding took one night).

What went wrong:

No music -- due to time constraints, and perhaps to our under-appreciation of how strongly a good soundtrack can manipulate the viewers' mood. If I were doing it again, I'd definitely add music (I'd avoid overly contemporary stuff, it doesn't age well. If possible, I'd use Hollywood-style orchestral sound, however, I'm not sure if suitable pieces are available as stock music.)