Yes, those asterisks just refer to a footnote that declares that "*Other names and brands may be claimed as the property of others." --> http://www.intel.com/content/www/us/en/legal/trademarks.html

They're tiny ® (registered trademark) symbols.

Kind of. They're actually footnotes (asterisks), referring to the same footnote. On this particular website it appears to be referring to the "*Trademark" link, which has the extended legalese.

In the standard Intel style (whitepapers, etc), trademarks to other companies are designated with an asterisk and a footnote to the effect of "These are trademarks from companies other than Intel. They own the rights to the name, and not us"