SSI are meant to be run by a Nginx filter when serving pages, they are not a form of HTML shorthand (like SASS is for CSS).
Still, on Linux/MacOS (and Windows, if you download it) you can use wget
to mirror you website. You will be requesting and getting all processed web pages that are (recursively) linked from the home page. Try with:
wget --mirror localhost:8080
or any other URL for your website.