No, GitHub primarily uses regular git on the backend. It powers all fetches and pushes, diffs, and most of the history traversals. Some functionality is provided by libgit2, and it's ever-increasing because libgit2/Rugged is often more natural to call from ruby code (though a lot of it is replacing old Grit code, not git itself).

libgit2 powers much of GitHub's desktop apps, with regular git mostly filling in any functionality still missing from libgit2.