Using our keys without our permission is circumventing our DRM.
Yuzu is a tool that enables you to use our keys.
It's illegal to distribute tools to circumvent DRM.
It's a massive reach, but it's a plausible argument—or even a good one if the judge is a technologically illiterate luddite. Beyond that, Nintendo is the kind of litigant that will drag out a lawsuit until the other party is forced to settle.