That being said, does the Devil himself have to die after Armageddon?
That depends on how you perceive the nature of god. Is god unable to act against his nature, so that he must take certain actions in order to remain true to himself? Or is he free to go off-script if he so wishes? The Biblical god has no equal in power and he cannot be brought to account, so the only person who could stay his hand is himself.
We know that god was not a stickler to the letter of the law, allowing humans to break the rules sometimes and not face punishment. So it seems as if he understands that rigid adherence to rules is not always the right way to act. If this is the case, then the Devil would not have to die at Armageddon. God can forgive him and let him live, without violating his own nature. I suppose he would need a very good reason for doing that, but it can happen.
As a non-believer, I can look at the issue from that angle. When I was a JW, I would have said that there was no way that Jehovah would allow the Devil to live, because Satan had directly challenged God's rule and caused so much suffering. And to be honest, just because God is willing to bend the rules for the sake of justice doesn't mean he would find any reason to spare the Devil. And if the Devil was unrepentant, it would make no sense to forgive him, instead of putting him out of everyone's misery.
That being said, we are left to wonder why God didn't just do that from the very start and save us the thousands of years of suffering and grief.