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