Nightly downloads are not a feature of Buildbot and need to be implemented
separately. A good place to start is
https://github.com/buildbot/buildbot/tree/master/master/buildbot/status/web

Also, here's the transcript of the maintainer's (public) response on IRC:

caen23: djmitche: http://builder.blender.org/download/ can buildbot do this, or is it a hack by blender?
djmitche: it's just file serving
djmitche: usually it's better to let Apache do that
djmitche: but they're just putting files in $public_html/downloads
djmitche: so yeah, buildbot can do that
djmitche: oh, no, sorry, that's custom
djmitche: Blender might be willing to share