The demo mentions the privacy concerns of third-party cookies, but does not mention that there are significant positive uses for such cookies. In the demo, reference.com sets cookies for thesaurus.com and dictionary.com, which are different domains run by the same operator. Such cookies allow the operator to provide customized services across the domains. Third-party cookies allow for richer embedded-content experiences. Video is a great example of that.
The revenue sites can get from third-party cookied ad networks is significantly higher than from unpersonalized third-party ads. Large sites like HuffPo and NYT are able to sell a lot of their premium inventory directly, so a big reduction there is likely to disproportionately affect smaller sites.
In order to do this, a browser (or extension) would need to track through which sites a 3rd party cookie was set, and only send the 3rd party if you're on that same site again. Else it should just pretend there is no 3rd party cookie.
I'd definitely install an extension that would implement this process.
This doesn't, however, block all tracking scripts, as some may get your IP via an embedded 1x1 gif or other request. There's still the issues of super-cookies, or Flash cookies, or scripts that embed a unique image in your cache and then read it out, etc. So for this I recommend AdBlock or Ghostery.
Edit: Here's aseful link on this topic: http://samy.pl/evercookie/