Is it possible to authenticate into Stack Exchange using this method? At the moment there's other methods such as OpenID, Google, Yahoo and Facebook, but it would be interesting to also have the GitHub authentication.
You can log into any Stack Exchange site using the credentials from any Open ID provider. Unfortunately, at this time, GitHub is not an Open ID provider, so you can't log in using those credentials.
Also, it's highly unlikely that SE would create a special login mechanism for GitHub accounts unless there was great incentive to do so; it would require resources (time, money) to fabricate a custom mechanism when one already exists for this specific purpose (Open ID).
If anything, I suggest that you urge GitHub to become an Open ID provider, rallying support around that initiative. Once they are an Open ID provider, you'll be able to login to any Stack Exchange site with those credentials and link them to your account.
This is definitely possible...
I login to
SO.com, etc. using my
mralexgray.github.com, which is my
gh-pages URL. I forget how I set this up... at some point in the distant past... but I will research it and update this answer.
It's worth noting that they do support OAuth3 it looks like...