Gists and Snippets
So this page is using the built in Hugo shortcode gist. It inserts the github script tag to pull the data from a GitHub gist. The file used is a list of links written in markdown.
This means you don’t need to rebuild the site to update the gist. A simple pagre refresh will do.
It also means you have no control over the HTML or styling of the gist’s content.
Alternatives
Instead of using markdown use HTML. You can add a css file to the gist but obviously this would be the same in every web site.
Another way might be to is to embed a git repo in your page.
There are different methods: you could use an iframe but the styling could not be used from the site in which is is embedded.
Maybe pull the repo like you do with a theme using git clone or git submodules. Submodules is always up to date (after a site rebuild I assume). This could be incorporated into a partial or shortcode.
GitLab Snippet
Just testing this html snippet
What’s interesting is that it has picked up the CSS background colour for the pre and or code tags.
To allow these to get the embed code they have to be saved as public in GitLab.