I think this is awesome, but I do not see the use case: Why would anybody register on my site to publish his or her gists? I would love to get my gists from Github published under my site, but for this case I would prefer a static site generator (hugo, jekyll) with a good theme for gists.
Now this had me curious. Is there someone out there who has actually created a theme/template website for a static site generator like Hugo, Zola, or Jekyll where you could use both the usual markdown and the actual code files themselves? It seems fairly doable based off the templating engines available.
On the other hand, Docker seems to be a bit overkill for something one could use a static site for instead if it's supposed to be self-hosted. It's even better security-wise. Otherwise, I wonder if one could upload a gist and have it run on the server through some unknown exploit.