To export the site-lib 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:
* site-lib[ResourceLoader|type=general|dependencies=mediawiki.legacy.wikibits,mediawiki.util|rights=hidden|hidden]|site-lib.js
You must have appropriate permissions on the destination wiki (including the right to edit system messages) and import from file uploads must be enabled.