Certainly, the emulator is written with the knowledge that most end-users will use it to play pirated software. Most screenshots of commercial games running in it come from end-users, however even if they provide some themselves, there are plenty of jurisdictions where accessing material you own (and even circumventing DRM in order to do so) on a different device is considered legal.
But all that aside; the distinction is - and has thus far been supported by the courts - that _they_ are not distributing any infringing material. If we ban things because they *could* be used to commit crimes, we end up on a very slippery slope to (reductio ad absurdum) banning Notepad, MS Paint, butter knives, hats, etc. Generally, we also legally permit things that can be used in a legal manner even if they're most likely to be used in an illegal manner. As Yuzu being a hardware emulator is perfectly capable of running PD demos without infringing on any of Nintendo's rights, it doesn't fall into the same category as things which can virtually only be used in an illegal manner, which we often do ban (various classes of weapons, drugs, CSAM, etc).
The emulator itself doesn't contain Nintendo's intellectual property. It's a completely original work by third-parties, as far as copyright is concerned. (We can philosophically argue whether emulators themselves as a rule infringe on one's intellectual property, since someone else had to do the original work of coming up with the hardware design, and that if all one is doing is figuring out how they did that rather than creating something new, are you violating their intellectual property? But that's not what this lawsuit, or even discussion is about). Instructions on how to violate the DMCA are legal as well; they're telling you how you can use hardware you own. Now, if it's specifically against the law in your jurisdiction to violate DRM measures in order to backup your software, or you don't have a legal right to tamper with your own hardware however you wish to, making practical use of that information may be illegal. But the information itself is not.
Don't get me wrong - I am generally against software piracy, especially the kind Nintendo is discussing. I think they have a right and a good reason to be pissed about someone leaking TotK early and folks distributing it en masse. I'd largely be supportive of an argument to not distribute ROMs for software which is presently being produced and available for sale. However, I'm also all for preservation. The fact that repeatedly, both Sony and Nintendo have distributed pirated ROMs in their own re-releases of old software because even they don't have access to the originals, speaks volumes to why the efforts of emulation and ROM preservationists is important. We see companies which own the rights to old games releasing versions they've downloaded from abandonware sites on Steam and GOG, because - again - they don't actually have the originals anymore. They bought the rights. They want to make money from it. They just can't actually do so without relying on the folks out there working against their protections and their DRM in order to preserve those titles. We even see companies distributing executables with CD-check DRM stripped by pirates, because they don't have the source code to compile a version without it.
And so the original point stands - Yuzu isn't doing anything illegal. Nintendo just wants what they're doing, to be made illegal. Or, more likely, Nintendo just wants to bankrupt them and force a settlement without a judicial ruling either way. If one has a problem with piracy of games, then emulator creators aren't the target of your ire. The folks ripping and distributing games are. It's just that, as a concerted effort that takes a lot of time and people, emulators are a much easier target than a thousand fly-by-night warez sites which can close and pop up as a new entity within minutes.
