I'm throwing this out there as someone who has been in similar situations...
Stares don't work. Not the way you think they do. Especially on an individual who is drunk.
Now, I will say this before I get into anything else...I'm very glad that you weren't injured in this situation, and I commend you on being able to get out of the way of danger in enough time to prevent yourself from getting hurt. There is a type of "sixth sense" that you aquire over time, mostly when being trained on how to be aware of your surroundings, and it sounds like you did a fine job of using this tool to your advantage.
Now, that being said, I highly, highly doubt that the reason the chair-weilding villain backed down was because of a "look". Again, as it was stated by someone else before, no one from this forum was there to witness what happened, and that includes me. But, I've been there too, thinking that I looked mean enough to send someone packing.
I can tell you that it's more than likely not the case.
Put yourself in the attacker's shoes. If you're angry enough to smash a chair into oblivion, is it really going to make you think twice about doing it again just because someone looks at you in a "don't mess with me, buddy" kind of way?
I can tell you this much, I think I would have to be pretty darn angry to break a chair like that in public, and I'm pretty sure most other people would be the same way. I know that if I were to be that angry, I wouldn't really care if Steven Segal was giving me one of his "bring it on" looks, or if it was Chuck Norris staring me down Walker Texas Ranger style. If anything, having someone stare at me like that after I've attempted to break that someone's face with a chair is going to enrage me further to do something even dumber.
Add alcohol into the mix, as I'm sure was the case, and you can throw all common sense out the window completely. When drunk, a person's bravado sometimes is too much to control even for the police. And I'm not saying that everyone is like this, but most guys you see in a bar that are willing to throw chairs around have at least been there before...so it's very doubtful that they are going to back down from merely a stare.
Their reputation is on the line: the whole bar is watching by that time to see what's going to happen next...if the guy were to stop now, what would everyone else think of him? And for what reason did he stop? Because someone looked at him as if to say "Stop, or else"? Certainly not....
Now, I'm not sure why the guy actually stopped. Maybe he saw a cop coming through the parking lot, maybe he realized that you weren't the guy he was intending on breaking his face, or maybe you really did spook him.
I'm just saying don't put all your faith in that one stare. Even if it did pull you out of trouble this time, there are others out there that just watch for people to look at them that way. Some people are confrontational, and are just itching to start a fight.
Instead, rely more on your ability to avoid unnecessary confrontation at all cost. If that fails, then use the tools that you have been given to physically stop the situation.