Font licenses are pretty clear about what you are and are not allowed to do with the font files you downloaded. For instance, you're not allowed to zip them up and post them on filesharing sites. It does not matter at all whether you include a LICENSE file saying "this is a nonfree font."
The problem is not that you're misrepresenting the font as copyleft when it isn't. The problem is that you simply don't have a license to redistribute the font at will: merely uploading the font to a public GitHub repo violates the license.
You have the right to serve the font from your webserver, and link it into your site via CSS. You absolutely have not been granted the right to redistribute the font in any other manner.
If you post a page on your site with "Like this webfont? Download here!" and link to the same URL that you are using to host the font for display purposes, you'd be violating the license. It's the same exact URL, but you can't post a clickable download link to it. It's not allowed, and if you do, they can at a minimum yank your license to use it at all.
Editing to add: trying to solve the problem by adjusting your LICENSE file is roughly equivalent to the "I don't own this!!" disclaimers that people put on YouTube uploads. They get DMCA'd just the same.
The intent often matters, but there's clearly a huge difference between your example of a "download here!" link and usage on either a website or within a GH-hosted repo.
When you say 'the right to serve the font from your webserver' -- in this case, 'your webserver' may simply be GitHub's web-server, a service they provide to you as part of your payment to them (either because it's part of the app you host on GH, or as a piece of the website hosted via GH Pages [0])...
Assuming that the font's usage for the repo'd app/site is OK per the license terms, then I'd be surprised if its availability in the repo would solely cause it to fall out of compliance with the license. I suppose that the licensor could, if they chose to do so, specifically include terms to preclude the usage of the font on any sites hosted with "repository or other open file listing indexes", or any other similarly restrictive arbitrary terms.
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.
In that case, it seems as though the rights-owner should simply take the standard route (even if suboptimal) to enforce their rights -- given the volume, they could likely work out a much better way to protect their IP (or automate it, in the worst case).
I'd be a little bit surprised if they cared a whole lot, given that finding the fonts is trivial for the reasons stated above. Almost comes across blog-spammy at that point, heh.
The problem is not that you're misrepresenting the font as copyleft when it isn't. The problem is that you simply don't have a license to redistribute the font at will: merely uploading the font to a public GitHub repo violates the license.
You have the right to serve the font from your webserver, and link it into your site via CSS. You absolutely have not been granted the right to redistribute the font in any other manner.
If you post a page on your site with "Like this webfont? Download here!" and link to the same URL that you are using to host the font for display purposes, you'd be violating the license. It's the same exact URL, but you can't post a clickable download link to it. It's not allowed, and if you do, they can at a minimum yank your license to use it at all.
https://processtypefoundry.com/help/base/webfont-license-agr...
Editing to add: trying to solve the problem by adjusting your LICENSE file is roughly equivalent to the "I don't own this!!" disclaimers that people put on YouTube uploads. They get DMCA'd just the same.