My two cents...
It is a questionable one.
Person A: Person who did the sucker punch.
Person B: Cell phone talker.
First of all you're dealing with the typical standard of use of lethal force. After the first punch was dealt there is an argument that B or a third party could have used lethal force under the premise of fearing great bodily injury. I would be surprised if B did not suffer serious bodily injury. If A did end up doing felony time for the incident then obviously there was serious bodily injury or possible death of B.
You're also dealing with an obvious size disparity between A and B. A being the much larger person.
What did B do wrong? He was on the cell phone in condition white. Second is conflict avoidance. We don't know what B said on the cell phone to A's female companion to set her off. By virtue of the fact I CCW as often as possible I make it a point to avoid trouble and be aware. Even in States with a stand your ground law with civil suit immunity such as FL I'm not going to have a Dirty Harry mindset. I don't want to be good friends with a homicide detective, CSI personnel and a DA. I also don't want to deal with the post traumatic stress associated with being involved in a SD act the required use of lethal force.
Several factors may influence your decision or make you more apt to use lethal force. If you're in a State with stand your ground or similar laws, you may be more apt and legally in the right for any SD act. Case and point, FL or MO. There's a high probability that if this incident were to have happened in FL or MO, A would have left in an ambulance, coroner's vehicle or been driven to a trauma unit by his female companion. OH is one of more liberal cesspool shall issue States which their laundry list of prohibited areas, I'd be less apt to use a firearm. Also if the pizza establishment serves alcohol for on premises consumption it is a prohibited area under OH law. In States like GA, NC and OH with a laundry list of prohibited areas, I avoid them. I will pass through them but that's about it.
The other question what if A committed battery against the owner or manager of the establishment? Yes, typically the castle doctrine is extended to the premises of a business. But keep in mind you're in OH which is a cesspool of a State to begin with.
Could the owner or authorized agent of the business get involved and intervened in B's behalf? Yes, it's their place. If someone is beating up a customer in my place of business, I would intervene as it is bad for business.
Would they have been justified? IMO looking at the video, yes. A showed obvious disregard of the life of B. While B was probably rude to A's female companion or said an offensive comment in regards to her rude behavior of cutting in line to whomever he was talking with on the phone that is not an excuse to beat the life out of him. IMO, using a firearm to stop A would have been justified. I would return no bill if I was on the grand jury or not guilty if a firearm was used to stop A and he kept on going after throwing the first punch.
It's a mindset or zen associated with self defense. It's like the late Pat Morita said as the Mr. Miyagi in one of the Karate Kid movies, "Best way to block punch is no be there." Same goes with being in involved in any type of situation, "Best way to avoid shooting or being shot is no be there."
The street rule of thumb with SD acts is this; never start it. The force used must be appropriate for the actions warranting use of any type of force. IMO, B did not start it or warrant the beating by being on his cell phone.