Is this amount of play in the rear hub normal? (video)

[Dickey]

This afternoon I rode the bike down the street and back to see how I felt about some new goggles. That was the first time I'd ridden without a helmet and the rear sprocket was making all kinds of racket that I'm not convinced is normal. I brought the bike back in the shop and took a quick video of the chain. There are definite clicks that are audible in the video from the chain/sprocket interaction and there is some play from the sprocket hub to the wheel, which I did my best to demonstrate. The bike is on the stand so I can clean and tighten the chain but the sprocket bit is unnerving and I want to make sure I'm not inviting trouble.

The video is an MP4 and can be found:

http://www.dickeysgarage.com/video/chainslack.mp4