In the rules it clearly states that the emulators allowed are Nestopia, FCEUX etc. Just to clarify (might be a dumb question), does that mean that you need to use the actual emulator, or does it mean that you are allowed to use an emulator running those cores (Nestopia, FCEU...)

I believe the ruling is that you have to use those exact emulators - there is a Nestopia core for Retroarch, but Retroarch is banned as it has lag reduction built in that isn't present on console. However, there have been some cases, such as with LeKukie, where specific variants on the emulators are allowed. It's easier though if you just use the standard emulators as long as you have access to some form of computer.