Read the Docs doesn't serve arbitrary files from your repository; it only serves the results of the Sphinx build process. So instead of linking to files as in your example, use the :download:
role. The role tells Sphinx to include the extra files in a directory in the build output.
So, your example modified to use :download:
might look something like this:
Open this :download:`example <../path/to/bar.tgz>` input file to see the following result:
Note that the file path is relative to the reStructuredText file where the role appears, not the HTML output.