I really don't see the problem it was not human, it was something that preys on humans and that publicly challenged Harry's new status as Mab's knight. In Arctis Tor and all of Winter for that matter letting it live would have been a colossal show of weakness. Harry is not Michael he does not ooze compassion and love. Don't expect him to bow down to non human bullies, which is basically what that Sidhe lord was. Was it murder? Sure. Was it justified in universe and the "best choice" ? Hell yeah.

So while we may or may not agree I'm pretty sure even the Harry we will see at the end of the series would have done the same, no matter what kind of epiphany he has along the way.