"He handcuffed him and made sure he stayed put until police arrived…"
Up here, displaying a gun and handcuffing someone gets you menacing and illegal restraint, and the perp gets a free ride home.
Are you sure about that?
You're allowed to use deadly force to stop someone in your home from stealing your stuff, or burning the house down. So long as you have a justification for why it was necessary.
Honestly, my view is things can be replaced. Do I want my stuff stolen? No. But unless I believe my life is in danger, I wouldn't exercise deadly force, even if sections 2, and 3 in New York Penal Section 35.20 - Justification; Use Of Physical Force In Defense Of Premises And In Defense Of A Person In The Course Of Burglary. - New York Attorney Resources - New York Laws allow me to.
However, I would in the case of someone burning my house down, since it endangers me and my family.