I know that this is really old, but GitHub Enterprise 2.6 just came out with pre-receive hooks. More information can be learned here: https://help.github.com/enterprise/admin/guides/developer-workflow/using-pre-receive-hooks-to-enforce-policy/.
This should answer the question originally posted, as this is something that gets set up at an instance level (thus, it is only on GitHub Enterprise) and will work for all repositories.
I am trying to develop a link to a secondary system that will want to get notified of all pushes to all repositories, and requiring manual set-up for each new repository will just be a matter of time before it gets forgotten.
As for this piece, another thing you could look into would be log forwarding on GitHub. You can read about log forwarding here: https://help.github.com/enterprise/admin/articles/log-forwarding. You can also control multiple log forwarding destinations as of version 2.6