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Formerly, there was two methods of download code in Github: clone or download as zip a .git repo, or upload a file (for example, a binary) for later download.
When download a repo (clone or download as zip), Github doesn't count the number of downloads for technical limitations. Clone a repository is a read-only operation. There is no authentication required. This operation can be done via many protocols, including HTTPS, the same protocol that the web page uses to show the repo in the browser. It's very difficult to count it.
See: http://git-scm.com/book/en/Git-on-the-Server-The-Protocols
Recently, Github deprecate the download functionality. This was because they understand that Github is focused in building software, and not in distribute binaries.