but if they use any code from the actual system, it’s illegal.

Actually, this is not the case. DMCA allows some amount on code to be duplicated, just not the whole thing. You’re not allowed to copy everything, but copying some code is allowed.

Also, the encryption key that was copied in Dolphin is just a random string of letters and numbers. That’s not copywritable, so no copyright infringement happened from including that in the software, regardless of what Nintendo claimed