Chrome and Chromium dropped support for the NPAPI plugins (Netscape Plugin Application Programming Interface) in favor of PPAPI (Pepper Plugin Application Programming Interface) so all plugins that use NPAPI (like GNOME Extension plugin) are just not supported.
The only alternative is using another browser that allows them (like Firefox) or asking the developers to move to PPAPI (unlikely).
NOTE: This is the blog post from the Chromium blog mentioning this, titled: Saying Goodbye to Our Old Friend NPAPI.
