My wife often leaves the house and forgets the dongle, because she stretches and walks a block or two before beginning her running workout. But each time she syncs her Nano she has to take it out to sync it. My thought was that between the built-in receiver and the clip, this would be a great replacement for her. But after speaking to one chat agent this morning and then seeing some of the comments here and the same info you posted from the Sport Kit page, I contacted a 2nd agent who confirmed this time the opposite from earlier, that you did indeed need the dongle. I then contacted customer relations and was informed that while they did not know they would find out and get back to me. However, all signs point to it not being built in. And while it is not so terrible, it is rather unfortunate, and may preclude us from replacing our 2nd generation Nanos which otherwise work just fine and require the dongle anyway.
I did tell customer relations that the image below is false advertising, as it misleads people to think that all they need is the sensor.
From
http://www.apple.com/ipodnano/features.html#fitness