This video is no surprise - stuff like this literally happens every day in NYC. I work in NYC and groups of unruly "youth" like this are an everyday occurance on the subway, especially when school lets out around 3 or 3:30pm.
These kids look fairly typical...which means they don't appear to be gang-bangers but they do get on the train in packs and look for trouble. Kids like this have no upbringing and are basically animals that are buoyed by a pack mentality....they are looking for someone to victimize to have fun (sad but true). The level of violence is really determined by the appearance of a victim and the victim allowing the situation to escalate.
The guy in the video acted like a classic victim - he didn't move, continued talking to them which escalated the situation and acted like a wimp with his body language and voice, which is why they kept at it.
The key to avoiding this is pretty simple and most New Yorkers know this...you should always be in Condition Yellow...act with confidence in all that you do and when you see or hear them enter the car (you will usually hear them long before you see them)...just pay no attention to them and move away to the other end of the car. If they confront you, just be firm but pleasant, diffuse the situation with a joke, etc. and move away. Don't give them an excuse to try anything. Always display unshakable confidence and you shouldn't have any problem.
Assuming for a minute that a situation like this did, through no fault of your own, escalate to the point of violence, and there was no way to leave the subway car, which would be the first option (there are exits into other cars on both ends of each subway car), I would have to agree with the previous posters...initiate the attack, pick the ringleader, and very quickly and with extreme predjudice...stop them in their tracks and ensure they cannot get back up...by whatever means necessary as a warning to the others. Just because NYC leaves you with few CCW options, it doesn't mean that you don't have any at all...
Just my 2 cents, that and $2 will get you on the subway...