Realistically, if you win the war, or even if you're a western power that quietly retreats after losing it, there's nobody responsible. And if you lose the war the winner decides who was responsible for your killer robot army. There's Nuremberg precedent for "both".

If you're the designer on the losing side you might get lucky and the winner will 'look to other way' of your crimes in exchange for your future services. Also a precedent from WW2.

Engineers and scientists are generally considered a "resource". The winning power takes them, if needed.

Scientists are generally not considered a threat to power (unlike high-ranked officials). For example, Piotr Kapitsa had his arguments with Lavrentiy Beria and Stalin. Instead of death (delivered for much smaller insubordination) he was gifted a rifle:

"Beria summoned Kapitsa who amazingly refused him: “If you want to speak to me, then come to the Institute.” Beria ate humble pie and took a hunting rifle as a peace offering. But Kapitsa refused to help anymore."

That's I guess the main point of the discussion. The terrible news, that usually the winners judge those who lost. And a huge part of war crimes can be left unnoticed. At the same time using AI-ruled machines gives a huge advantage and increases chances to win. That scares.

We already have systems like that, whereby the accountability is intentionally so diffuse that no one can realistically be held accountable. Was it the programmers? The people who provided the programmers the specs? The military who set the kill parameters?

Well the answer is everyone on the losing side. How the punishment is carried out would probably be the same as in WW2. Prison time for most, to varying degrees, more severe punishment to main leader, probably limited clemency to the highest ranks so they can work in other countries to pass on their knowledge and skillset.

I speculate

There is no need for robots to have that sort of issue - https://en.wikipedia.org/wiki/Land_mine

If the robot is perfect, then there is no one left to prosecute a war crime. It's only a war crime if someone can accuse and prosecute, thus only losers commit war crimes.