doc2git is a simple web app which lets you generate a Git repo from the revision history of a Google Doc.
Every revision to the doc becomes a commit to a plain text version of the doc in the Git repo, with the correct author and time.
It's web based since it has to do the OAuth dance with Google to use the Google Drive API, but it runs completely client-side from then on.
The only benefit of the hosted version is that the OAuth setup is already done. If you're ok registering an OAuth app with Google (instructions in README.md) then it's trivial to run yourself. Given that there's no fine-grained permissions on Drive - it has to ask for read only access to your entire Drive just to access one doc - I completely understand wanting to run it locally.
[1]: https://github.com/repography/doc2git