They require GitHub, so they can track the number of Pull Requests you did in October.
That would also be possible on Bitbucket where I do all my public work... :(
But Hacktoberfest is a GitHub only thing, right? It's a partnership between DigitalOcean and GitHub to just encourage more open source contributions.
You are right that there's nothing stopping DigitalOcean to include support for GitLab or Bitbucket, but after a few years of Hacktoberfest, it doesn't seem like they are interested.
I did not even think about the reasons, honestly.
We're a place where coders share, stay up-to-date and grow their careers.
We strive for transparency and don't collect excess data.