GitHub link to Nintendo's claim - all the details you need are here
The emulator forks which are being taken down are as follows:
Despite this, the one fork that continues, and will continue without takedown is Ryubing - by Greemdev. This is created by an original member of the Ryujinx team. It's safe, the code is beyond reproach (and violates zero laws or Nintendo code) and actually brings helpful updates.
Still...shitty news. And more indication that the Switch 2's architecture will be damn similar to that of this current Switch. Them taking emulators down means the upcoming games have a solid chance of being emulatable on release. But...that's my own (and others') conjecture, so we'll see when the time comes.
What gives them the right to take down emulators? It's just code someone wrote that happens to be able to interpret bytes from a switch cartridge?
Why wouldn't they take down a company like analogue for example for making a hardware level gameboy emulator?
IIRC, part of the argument is that Switch games are encrypted, and the emulator uses real Switch keys to read the games. So Nintendo claims that by using official Nintendo Switch keys, it is violating Nintendo’s copyright and is subject to DMCA claims.
The argument is shaky at best. But the problem with DMCA is that combating it actually requires taking the claimant to court. So that’s a prohibitively long and difficult process, just to be able to go “hey Nintendo doesn’t actually have any claim here. Restore my repo.” Especially when Nintendo has a known history of drawing out long legal battles to exhaust defendants’ time+resources.
The patents on the Game Boy hardware expired years ago, so that's what gives Analogue the right to do what they do. As for these Switch emulators, I have no idea, but I'll guess it's just Nintendo trying to scare people without their own legal departments into complying.