It's a pity we don't get to see what happened before, so we can get a better idea of the level of threat. Were they harassing him and threatening him before this, or did they just run in and grab some stuff? If they threatened him, were weapons involved? Did they touch him?

These things can make a big difference to if a jury will find his actions justified or not.

What could be bad for the Asian guy, is that it looks like he kept stabbing when the already hurt thief was trying to get away. I haven't stepped through it frame by frame, but that's what I see at a glance. When he made that last killing stab to the neck, was he still under threat, or had the threat already been subdued? I think that's what the jury will be trying to establish.

I'm just speculating on what a jury might say here. I think it could go either way, and the Asian guy should get a really good lawyer.