Being the minister of defense gives you culpability for the military actions the ICC has decided are war crimes, I'd think? But I am not an expert in international law, just don't find it surprising.

Yep, commanders are responsible for the actions undertaken by their troops.

It's called Command responsibility or sometimes the Yamashita principle/doctrine, after a Japanese general who was executed for horrific crimes committed by troops not even under his command, but in his area of responsibility (they were naval troops in the Philippines, he was commander of the Philippines, the navy and the army hated each other; he pulled out of Manilla in order to wage war in favourable terrain, the naval infantry commander refused to follow him and fought a brutal urban battle that destroyed the city, and on purpose killed more than a hundred thousand civilians).