The languagetool.org website is checked in to git at https://github.com/languagetool-org/languagetool-website. Every LanguageTool committer has write access there. Changes automatically appear on the website after at most 5 minutes after check-in. The website is based on simple PHP files with some includes that create the navigation.
This Grails-based website can only be updated by the admins with direct server access. See server documentation for details.