Obviously he felt uncomfortable enough to put him in a choke from behind and hold on to it long enough to kill him. If he had been attacked or threatened, then I could see it being justified, but it really wasn't.
In a situation like that people who are acting crazy or yelling things are usually either having some kind of mental health issues or they want attention or something. I was in the grocery store a few months ago and the clerk at the self checkout started talking to himself saying some odd things and punched the ground. I think I showed remarkable restraint by not choking him to death because he was making me feel uncomfortable.
The first thing you do, or if you don't you should, is assess the situation. You should be able to determine if somebody poses an actual threat pretty quickly. Calculate the risk of what action you're going to take. If you have to get into a physical confrontation, be ready to get hurt or hope that if this person uses drugs they don't have anything on them that could poke or stab you, they won't bite you or something else like that. Once you do that, then take appropriate action, which is usually letting the authorities know. NYC has transit police who deal with this.
So physically confronting somebody who is having a bad day and talking crazy is something that isn't advisable. For a variety of reasons. The sad part is people are cheering this guy who essentially got away with homicide and treating him like a hero.