It's tough to judge the morality of the execution scene when the circumstances are so ambiguous.
What exactly is a "black hole" in the Abramsverse? It clearly has no relation to anything in real science. Sometimes it sends you back in time without a scratch, other times it kills you. Why does it do one thing one time and the other thing another time? Space magic, I guess.
If it was unclear to me, it was probably unclear to Kirk too. So he made sure that the genocidal war criminal didn't survive to fuck up the universe again. Given what he knew and didn't know, I don't see any moral issue at all with it.