Gaming

Same reason emulators are allowed. As long as the emulator doesn't use Nintendo's literal software/hardware or schematics, and as long as the emulator doesn't traffic in illegal file-sharing, it is allowed. Or at least, it exists in a legal grey area. And Analogue's pitch is original hardware, essentially rebuilt from scratch using FPGA technology. You still need actual Nintendo 64 carts to use this device. Or at least, that is how it is marketed.

I think the recent emulator shutdowns by Nintendo were more about software piracy. The devs knew that their emulators were being used to play unreleased Nintendo games. The emulators themselves may have been safe and legal, but the devs are mostly just volunteers, or small time operations running on a patreon. As soon as Nintendo applied even the smallest amount of pressure, the devs caved, because they don't want to spend their entire life savings and then some trying to defend software piracy on principle. Me thinks that Analogue would actually put up a fight if Nintendo tried anything, and that's why Nintendo doesn't try anything.