The license I linked expressly forbids "distribution of the fonts through file sharing services and online version control repositories accessible by the public"

It would be the same if you publicly hosted a zip file containing your site's contents, including the fonts. Or offered an open read-only FTP account to your /web/ directory. Or any number of ways to make the font available publicly that isn't via a web browser making a request triggered by a CSS rule.

If it's a private repository, I expect you'd be in the clear, since it's just acting as a very fancy webhost, and you can obviously upload your fonts to your webhost.