Murder does not imply or solely include innocent people. I linked the definition and you still got it wrong. Well done.
I'm not expecting you to turn the other cheek, I'm expecting you to turn them in, because it most certainly is murder if you're killing them at a point in time where they're no threat to you and other options are available. You're essentially killing someone because you're paranoid that you're not going to be able to call for help in time, despite their being no basis to that apart from "oh God what if he wakes up and escapes and runs away before I can call for help from the phone in my pocket/next door neighbors and then tomorrow night he comes back to kill me I obviously have no recourse but to murder him". And really, if someone is both unarmed and unconscious, it doesn't matter if he's Jackie Chan, at that point in time he poses no threat to you and the logical thing to do would be to call for the police. And hey, as long as we're imagining obscure, remote scenarios, here's one that's more likely: the guy has a buddy who's watching his back outside, as many good thieves tend to have, and then he find out you killed his buddy. If you're lucky, he'll go cry in the corner of a bar and badmouth you. If you're unlucky, not only do you have the exact same 'escaped thief on the loose trying to kill you' but the police probably aren't looking for him. There is a possibility of this happening if the burglar gets caught and turned into the police, but the possibility is even more remote.
But like I said, they're both improbable scenarios that the police, people trained to deal with criminals, are prepared to deal with via witness protection programs and the like. These people, who are trained to deal with criminals I'd like to remind you, can take care of the situation non-fatally for all parties involved, most of the time. Why wouldn't you go to them? Oh yeah, because you're worried the man that is unconscious and tied up might suddenly become not unconscious and not tied up and come and kill you, so logically you can't ever, ever use a cellphone or call for help from your front porch or visit a neighbor or any number of things that don't include murder and yet still end with the thief not being a threat to you outside of a remote, improbable chance that your thief can manage to wake up and untie himself and escape and has the stomach for murder and won't think twice about returning to the scene of a crime he was caught at.
Because that's obviously what's going to happen if you leave him alone for even the second it takes to call out your window.
Basically, what I'm saying is that the law exists for a reason, to protect people. It will protect you. Paranoia helps no-one and you are not judge, jury and executioner. The man has a right to life, poses no threat to yours outside of worst-case scenarios, like the kind that can occur when you eat dinner (you might choke to death oh God never eat again) and you have the ability to turn him over to the police, quickly and easily. Are you saying you wouldn't, just because all the above might happen? Because that is the most ridiculous thing I have heard in a while.