To export the ExtendedNavigation gadget, click on "Download" button, save the downloaded file, go to Special:Import on the destination wiki and upload it. Then add the following to MediaWiki:Gadgets-definition page:
* ExtendedNavigation|ExtendedNavigation.js|ExtendedNavigation.css
You must have appropriate permissions on the destination wiki (including the right to edit system messages) and import from file uploads must be enabled.