By "conviction", I understood them to mean a kind of blindness -- an unshakeable belief that what you are doing is right, regardless of what others may believe. That kind of conviction is orthogonal to intention to harm another person. I took the entire thrust of their argument to be that intention to harm another person is neither necessary nor morally important for evil. But that is not how most of the West sees it (as evidenced by the distinction between murder and manslaughter that I pointed out).
If, when they wrote "conviction", they in fact meant "intention to harm another person", then I agree with them. But in that case I'm not sure why they posted their comment at all, since that (namely, the thesis that intention to harm is morally important when actions cause harm) is already the accepted norm, at least in the West.
(I still think it's a bad example even presented like this, and I disagree with GP, but your example seemed wrong)
Manslaughter is when you kill someone without conviction and/or delusion. You can hit someone without the conviction that you need to kill them and they fall really badly and die.
Murder. You can hit someone in self defense where you have no conviction that the person must be killed (because for example they say you had sex with their wife, but you in fact know you didn't, it's a misunderstanding), and you don't have any delusion (you know the attacker is delusional in fact). And then you defend yourself and he dies because he hit his head badly on the way down.
Because that is the only way I can interpret your examples so that they correspond with the legal distinction, which is based on intent to harm and TTBOMK never mentions "conviction". If so, we're in full agreement, since that is already the accepted Western norm and my original comment was based on a misunderstanding, and unnecessary.
But also if so: I'm puzzled why you chose to swap the natural and original word "intent" for a different word ("conviction") that is easily misinterpreted as a quality orthogonal to intention to harm, and about which an interesting but fundamentally wrong argument is periodically made (namely, that it, plus power are sufficient for evil, without any need for intent). I'm also puzzled why you made the initial comment I replied to at all, since it's then a defence of the absolutely uncontroversial status quo. It's like posting that you believe in gravity.
No, I mean "the probability function you ascribe to your beliefs". A person who believes something very weakly doesn't put on a suicide vest to blow up civilians in order to further this belief. A person with a strong belief might.
If you believe this, your beliefs are out of step with essentially every Western justice system, which hold murder to be a worse crime than manslaughter. The difference between them is solely the intention.