Fair use has nothing to do with this. Fair use has to do with distributing a copyrighted work. Emulators are (ideally) running completely original code that isn’t copied from the company’s source code. This is why, for example, PCSX2 has you use “your own” PS2 BIOS instead of including it.

The PS2 BIOS is copyrighted, so it’s illegal to distribute it (and it’s never been “fair use” to distribute it). But it’s not illegal to do whatever you want with it (including dump it) as long as you own the console you’re dumping it from and as long as you don’t upload it to the internet for the purpose of distributing it to others. As far as the law is concerned, you bought the console and can do to it whatever you wish, provided you keep it to yourself and don’t distribute it to others.

Games fall under the same category. You’re free to dump your games and play them however you wish, provided you don’t distribute the dumped game to other people. However, companies are also free to implement measures (DRM) to stop you from doing that as much as possible, likely because they know more people would illegally distribute them if they didn’t.