I looked through the repo for the nodegit.org homepage in an attempt to submit a PR, but it doesn't look like that content is maintained here.

/* http://www.nodegit.org/ */
// Load in the module.
var git = require('nodegit'),
  async = require('async');

// Open the repository in the current directory.
git.repo('.git', function(error, repository) {

In this example taken from the homepage, an exception would be thrown because there is no "repo" method on the git object, or it's prototype.

The correct usage should be git.Repo().