Well, it uses Windows Media Player, but I don't know what the problem is. (It could be that you need to enable cookies for that site, but I'm not certain that's the issue.)
Anyway there's actually a better alternative. Go
here--minimize or kill the DVD-page pop-up/under--and that page should not only work, but give you access to a bunch more shows. (The one on the original link is just a "pop-up video" version of "Spin Fun Knowin' Ya.")
Enjoy!