The OLD Apple iPod Universal Dock
Well, sort of. I believe your link referenced the NEW Universal Dock, the one that has a smaller, rectangular infrared window on the front. The one I have is the older one, with a larger, round infrared window. I can only vouch for the latter, which I know outputs video from the 3rd gen. Nano.
The older one (round IR window) has an S-video jack, a regular iPod connector (for power and charging), and a 4-conductor 1/8" jack that outputs video as well as left and right audio. 🙂
The newer dock (rectangular IR window) has the iPod connector for the power and charging cable, but doesn't have the S-video jack, and only provides audio on the 3-conductor 1/8" jack. Apple prefers users get the special A/V cable and use it for video with this newer dock. 🙁
I got my older model from eBay, once I heard that it would work, and I think I ended up paying around $20 for it.
As an aside, what's fascinating about the 3rd gen. Nano is that it actually outputs video in THREE forms: composite, component, and S-video. Quite an amazing little device!