Copying of any Nintendo game is illegal and is strictly prohibited by domestic and international intellectual property laws.
This statement is false. Regardless of how much Nintendo might wish it to be otherwise.
"Back-up" or "archival" copies are not authorized
This statement is true. However, unauthorized copies are not necessarily illegal copies, again, regardless of how much Nintendo wishes it were true. Copies made for the personal and private use of the copier are not infringing.... any more than driving over a hundred miles per hour on one's own private property is breaking any speed limit laws (presuming, of course, that one has enough road on their property to do this).
and are not necessary to protect your software
This statement is clearly a case of Nintendo saying something that they can only hope people will blindly believe. At best, this statement is true only if one realizes that they may be talking about "software" in a larger context than just the content of the disk(s) that came with the game. In that light, the "software" is actually Nintendo's, and in that context, their statement is completely true. It's just grossly misleading.
Violators will be prosecuted.
If something is copied for the private use of the copier, just how can they even begin to prosecute something they wouldn't know happened?
Things equal to nothing else are equal to each other.