The forks aren't actually automatically taken down in most cases. The claimant must list every individual fork in the claim. Which I love, because it's kind of petty but still following the DMCA to the letter.
Here is an example[1] of the form claimants must fill out.
> Each fork is a distinct repository and must be identified separately if you believe it is infringing and wish to have it taken down
IIRC it took them a couple months to get through all of the Yuzu forks after the initial DMCA and lawsuit. I doubt there were nearly as many forks of Ryujinx, though.
Here is an example[1] of the form claimants must fill out.
> Each fork is a distinct repository and must be identified separately if you believe it is infringing and wish to have it taken down
[1]: https://github.com/github/dmca/blob/master/2024/05/2024-05-3...