It looks like GitHub indeed does not offer downloads of generated sites.
You can try to use web archiving tools (like wget) to get all content from the generated website, or generate the HTML from a local repository using Jekyll.
I'm sure you found https://help.github.com/articles/setting-up-your-github-pages-site-locally-with-jekyll which has instructions for Mac, Windows and Linux.
I hope this still helps a little!
Digital Scholarship Librarian
Centre for Digital Scholarship, UBL
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