Here is the simplistic explanation of the important aspect of this decision:
1. The Digital Millennium Copyright Act (DMCA) protects "Internet Service Providers" (including most blogging websites)from liability for various material posted by third parties. For instance, if a third-party commenter were to post a defamatory comment on this site, neither myself, nor the site's operators would be legally liable for the other person's comment, since we wouldn't be considered the authors of it. It prevents our liability for 'republication' of the third-party comment, even though it appears on this site.
2. However, the DMCA does not extend its liability protections to intellectual property (IP) claims. For instance, if somebody alleges that a thrid-party posted a copyrighted video to this site, we would still be legally obligated to take it down - provided that we were given notice and the video posting doesn't otherwise comport with fair use.
Why did the DMCA carve out an explicit exception for IP in its liability protections? The usual reasons - Big media lobbied Congress to include that provision in order to protect its turf. There is no such thing as an organized political lobby for those who might be libeled in the future. (As a result of the IP exception under the DMCA, the development of the Internet still has been unfortunately slowed...but that is obviously a much bigger debate and discussion for other posts on this site and elsewhere.)
So the vital question then becomes: What is 'intellectual property' for purposes of interpreting the DMCA? Some states have a mutant form of IP protection called the 'right of publicity'. They also have other laws under the rubric of 'unfair competition' or 'trade secret' laws that also serve as a mutant (and broader) form of IP protections. Then there are also state 'common law' forms of copyright and trademark protections that you may read about from time to time.
So in other words, state concepts of IP are often defined far more broadly than federal forms of IP. If you were to accept the broader state notions of IP, and then allow those notions to dictate the meaning of the DMCA, that would mean that the DMCA offers less and less liability protections to Internet Service Providers. States would eventually be able to define "IP" so broadly that the DMCA would effectively become a meaningless hollow shell - offering no real protections for anybody.
Fortunately, the 9th Circuit saw through the nonsense, and said that the DMCA still offers liability protections for all forms of state IP claims. The only exceptions to the protection for websites under the DMCA will be for IP that is recognized under federal law.
Well done 9th Circuit! There is still plenty wrong with federal IP and the DMCA, but at least they have seen fit to minimize the damage in this particular instance.