There are two things in conflict that apply to Dolphin, and in general to post-DRM console emulators:

• It's illegal to create or distribute a device which circumvents DRM.
• It's legal to ignore DMCA restrictions for the sole purpose of making things interoperable, like running software on machines it wasn't originally created for when you'd be able to run it on the machine it was created for.

The wording in the legislation is sufficiently vague that it's not obvious whether it's illegal to create or distribute a device that circumvents DRM for the sole purpose of interoperability. If a case goes to court, it could set a precedent that has to be applied in the future, or it could be settled out of court to avoid setting a precedent, and so far, there's no case law setting a precedent.

When Nintendo asked Valve not to allow Dolphin onto Steam, despite what some people were saying, the decryption key was known to be there, and the Dolphin team had legal advice that it was reasonable to expect that the interoperability exceptions had more power than the DRM circumvention restriction. The decryption key is a so-called illegal number, but these are probably not actually illegal, and you can see several examples on the Wikipedia page about them. Nintendo ended up taking no action against Dolphin, and it wouldn't have been a good case to try and set a precedent with as there weren't obvious damages now it's been so long since the Wii stopped being sold, and because the Dolphin team have historically been so diligent about stamping out discussion of piracy in their official communities, making it hard to argue that it's intended as a DRM circumvention device rather than an interoperability tool. Also, Dolphin's never taken donations, easily covering all their costs with just basic ads on their site.

Yuzu's a bit of an easier target. For a start, it's got a Patreon, and that makes it easier to paint its developers in a bad light as they're getting money (as well as meaning there's actual money to recover). They've also got data to back up the suggestion that lots and lots of Yuzu users are pirating games instead of just playing games they've already got a disk copy of. In a sensible world where laws are applied fairly, there's an easy argument that hoops to jump through like requiring the user to provide Switch firmware show they're not trying to make piracy easy, but it's not like Yuzu will be able to muster up enough money for lawyers to match what Nintendo will be spending.

The worst thing that could come out of this is a decision that interoperability isn't an excuse for circumventing DRM under any circumstances, as that'll have serious consequences for a bunch of other projects, and Nintendo are likely to want to push for this precedent to be set rather than accepting an out-of-court settlement. On the other hand, Nintendo could mess up and get the opposite precedent set, although if it looks like that's going to happen, they're likely to drop the suit.