After your opponent does the 2 handed shove, your move should be to kick him in the testicles as hard as you can. If your opponent goes down, then you ended the fight before it could really get started and you walk away.
(many years of martial arts)…
To modify your approach a bit, you shouldn’t pause for the “if your opponent goes down…” piece, but should already be on other follow-ups. Never wait for the results of any strike, always assume it wasn’t enough and already be continuing with follow-up combinations and actions.
Our “bread and butter” was a low feint kick, and immediate transition into flurries of face/eye/neck strikes while their eyes and hands are usually flinching down in reaction to your kick.
The loser of the fight was plain stupid in picking the fight, then dropped his keys or whatever, and was only expecting a kids schoolyard scrap. The winner looked like he probably pay-per-views MMA fights and has maybe had a MMA class or two at the gym with his buddies.
Yeah but what about “overkill”. How bad do you really want to hurt someone over a shoving match. Granted, a mugging you do whatever is necessary but why “devastate” someone over a shoving match? Your approach sounds a lot like the Ed Parker/Kenpo method, overwhelm and devastate. Whenever I took a class like that in the back of my mind I was thinking, is it really necessary to kick the guy five more times after you already kicked him in the nuts?
Conversely… what about the “danger mind set”. Self defense books will tell you “allways be aware of your surroundings”… “allways be prepared for danger.” They never said specifically, live your life in extreme paranoia, but after 257 pages of “what might happen” it does make you start to be paranoid. I decided, after reading one such book (I’ve read a few) that I rather, in a 20 year period, get beaten up/mugged once than live the whole 20 years constantly being afraid of danger around the corner. I am not talking just philosophically either. Reading that book really did make me scared, I was starting to see danger around every corner, literally.
Both of them were losers.
In the dojo I have attended we are taught that fighting is a last resort. One has to stay alert, keep one’s guard up, but if there’s a chance you can back out, or talk yourself out of a situation, OR GET AWAY BY RUNNING, you take it. The sensei once said there’s no shame in running.
It looks to me like those two idiots talked themselves into a fight, not out of it.
At least when I trained, in American Kenpo we learned several different techniques for the two handed shove. One of the first techniques I learned outside of the beginner class. I don’t remember the name. Use your hands to come underneath the push and spread his arms, two handed spear hands to the lower stomach, drop to one knee while slapping his knees apart, groin strike, hook his leg with yours and drop him straight back on the ground. And the above takes about 2 seconds and of course you can really do damage if you keep going . 
I agree with most that you either walk away or when the other motherfucker is running his mouth, take him out. Don’t get into the escalation dance, and if you do get into that dance be the first to break the cycle.
No news yet if the guy who posted the video has been charged with filming in portrait rather than landscape. I know that’s got to be a crime.
As others have mentioned, the loser was the one who instigated it, driving all the way down to confront the other guy. So while the hell did he have his phone in his hand, especially if he instigated it by getting into the other guy’s face and finally shoving him? I guess we can assume he wasn’t all that bright to begin with.
I was told that all you need is contained from 1:30 here
I had a friend (liver cancer) who was a scary looking biker most of his adult life. He once told me he’d only ever been in one fight. In his one fight he bit off one of his opponents fingers. With that in his rep (and being a huge, scary looking sonofabitch) he never had to fight again.
Your sensei has obviously never seen some of the joggers in spandex around here…
Here’s the way you win a fight every time with a trash talker.
Note to self: When fighting don’t go looking for lost objects.
Someone should have punched the person videoing. How hard is it to keep the action centered? And horizontal you a-hole not vertical.
When I see real fights like this, I’m always surprised that nobody goes for biting when they’re really close. How easy would it have been for the guy pinned to the ground to grab the other guy’s head and just take a chunk out of his cheek? Is it harder than I think to bite someone while grappling or do people just not think of it?
Sure, if you don’t really care if they have any blood borne diseases…
“Stupid” isn’t blood-borne. Even if it were, it’s too late to worry about it for both guys.
Regards,
Shodan
It’s certainly a grey area, but basically because anyone unhinged enough to be determined to be violent with you is also likely to have a knife in their back pocket, or walk to their glove box for their pistol, or grab the nearest brick to pound you with. Relying on unwritten ‘playground honor’ for someone to cry uncle and give up is very risky.
This isn’t saying gratuitous overkill is the way, but use enough of it to be sure that you can safely runaway from the confrontation without the danger of uncontrollable escalation.
Example: A classmate had a drunk in a bar start a fight. The drunk took a swing, he blocked it and kicked him in the belly. The drunk crumpled holding his belly. It seemed that was that. But he was only feigning enough to pull a knife from his pocket and came up and slashed our classmate’s neck, almost killing him.
Yeah, I’d rather get in “shoving match fight” with a MMA superstar and get my ass totally kicked… than… get in a fight with some random stranger who has almost no fight training but has no problem about picking up a brick or a knife. It’s the person with no conscience who is the most dangerous.
My last fistfight was forty years or better ago, and I do not know any martial art. I agree that the key to the win is to realize that the fight is on, and the chest beating verbalization is over. Once you decide to fight, all out attack is the only way to win. In this litigious society, the winner of the fight is likely to lose the ensuing lawsuit.
I will go to any length to avoid a physical altercation. It just isn’t worth it, and I am a little old man. However, If I am forced into self defense, it will not be a fist fight.
If I can add on to this. Ed Parkers method was definitely to overwhelm. 5 very quick immobilizing strikes instead of the one knock out punch. The thing is, you can stop any time you want, assuming you’re in control. You don’t have to do the FULL “leap of death”. 
The other piece was that American Kenpo was born out of the Hawaiian melting pot and taking on simultaneous attackers.
But as my instructor always said, you need to make sure the guy is down and stays down. Don’t give the perp the opportunity to pull a knife, gun, break a bottle or his buddies bushwhack you. An extra groin shot is just insurance.
From my quick skim it looks like the loser was looking for a fight…so, the best thing he could do to not lose would have been not to start it up in the first place, and to de-escalate before it came to blows.
If you have to fight though, and you aren’t and haven’t trained then the best thing is to get it over with as soon as possible. Speed and aggressiveness will often win a fight in the first few seconds. Most people don’t actually like to fight, and don’t really want to…they just sort of think they have to, so they back into it. A lot of bar fights are between two guys who are being assholes, don’t really want to fight, but don’t want to back down either and appear weak, so end up sort of escalating things to the point where they have to…and then do it badly. It helps to be mean and willing to take as well as dish out pain, of course, but being in control of yourself and your emotions as well as knowing what you can do, what to expect and being prepared goes a long way in these sorts of situations. Myself, I’ve been in my share of bar fights over stupid shit, but I do try to avoid them when I can if I can talk my way out of them. If not you need to pull the trigger yourself on your own terms and do it fast and with as much surprise as you can muster. I try for take downs and pressure/locks unless the guy looks like he knows what he’s doing (because frankly, if you go for a knee you are probably talking about serious damage…and groin kicks are pretty much what everyone expects, so they rarely actually work as an opening gambit), in which case I go for maximum aggression and damage as quickly as I can…or freaking run away screaming like a little girl. 
What was that line from the old movie Wargames?
A strange game. The only way to win is not to play.