Why would you expect "mouse-free control" for an application whose user experience is fundamentally designed around a pointer?
Of course, GitHub for Mac should leverage Mac OS X's Accessibility infrastructure so it works with assistive technologies like VoiceOver and full keyboard control (I hope it does!) but I suspect from your comment that's not what you're looking for.
Of course, GitHub for Mac should leverage Mac OS X's Accessibility infrastructure so it works with assistive technologies like VoiceOver and full keyboard control (I hope it does!) but I suspect from your comment that's not what you're looking for.