Moral justification for the execution of criminals of war?

[The Architect Of Fate]

Because rights are tiered.  They're founded on basic principles, and then refined tier-by-tier.

Root node rights are things like the right to life, to the pursuit of happiness, to liberty, and so on.  If we form a financial contract and you violate its terms, the problem is that the violation of that derivative right (the right to be paid for my work re a contract, say) may give way to peer nodes, i.e. different expressions of those more fundamental mores.  If I can't get my money from you, then the system will restore some kind of moral balance by limiting your liberty, for example.

But when the violation is agains those fundamental rights, then there ARE no peers.  You can't really restore balance for the life of a child by imprisoning someone, because liberty is not more fundamental than life, and no appropriate peer derivative can be found.

There is one more type of node that I haven't mentioned-- a duplicate.  Since there's no peer node for a death, then the only really just punishment is death-- if, at least, intent to kill can be demonstrated.

Death pays for nothing and you can never pay for life. And killing killers is not part of any reasonable social contract and no breach in said contract equals death.