Update doc build to use latest GH release system.

It looks like GH has deprecated the download system that we were using. This fix just updates our doc build to point to the new system. Here's the blog post for reference:

https://github.com/blog/1302-goodbye-uploads

This resolves many errors that appear when running 'make linkcheck' against our docs.
Merge pull request #9125 from cachedout/gh-doc-fix

Update doc build to use latest GH release system.