Either:
Open a terminal.
If you haven't already, enable the Canonical Partner Repository:
sudo add-apt-repository "deb http://archive.canonical.com/ubuntu oneiric partner"
Install the package adobe-flashplugin.
sudo apt-get update && sudo apt-get install adobe-flashplugin
Or, in case that doesn't work:
Open a terminal.
Install the Chromium Browser.
sudo apt-get install chromium-browser
Watch the video in Chromium.
The issue here seems to be some versions of the Flashplugin in combination with Mozilla Firefox. While I was able to solve this by installing the Flash version mentioned above, this has never been a problem with Chromium.
Tested on 64-Bit Ubuntu 11.10