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!