The jam page says to use a public github repo, but I'm more familiar with using other versions of git like Gitlab. Is having my project hosted on Github a requirement in order to be a valid entry in this jam? 

It's a GitHub sponsored event so yeah.
Tehnically you can still keep on using your prefared version control as long as you also create repo on GitHub with at least one commit at the end.
Since it's a public repo you don't have to push assets you don't want or not allowed. just the code.