GoKawiilEmulators are not illegal to use; it's how you acquire games for them that can create problems. Technically, the only software you're legally allowed to play on an emulator is something you've developed, or physical games you've purchased and then converted for emulator use via a process called ripping or dumping.
The game data you extract through this process is broadly referred to as a ROM, though for disc-based systems, it's technically an ISO file. Dolphin's FAQ section about where to download ROMs plainly states: "You don't. Buy games and dump them with a Wii." Any other method of acquiring ROMs violates copyright laws, including the DMCA (Digital Millennium Copyright Act), and is considered piracy.
Because of this, many companies have tightened restrictions or even taken legal action against emulators, with Nintendo being one of the biggest players in the fight against emulation. In 2024, the company filed a $2.4 million lawsuit against the creator of Yuzu, a Nintendo Switch emulator, which Nintendo said created "piracy at a colossal scale." A year prior, when the Dolphin emulator was set to be released on Steam, Nintendo served Valve with a DMCA notice, indefinitely postponing the release. And further, Nintendo's page on intellectual property makes it clear how the company views the matter.
With this kind of precedent set for Nintendo-focused emulators, it's possible Gecko could run into trouble down the road. However, much like Dolphin, so long as the importance of legal ROMs is emphasized, issues are only likely to arise if the emulator is offered for download in a marketplace like the Steam Store.