"The boy probably would have left the train if the conductor had radioed for the police anyway, he wouldn't want to hang about and get arrested"
"On the other hand he might have continued to not give a shit..."
In which case he would have still been there to be removed by the police, who do have the training and authority to get him safely off the train without harming any other passengers. The BigMan pushed him into a woman or bashed her himself and put her, her kids and other people at risk.
I just cannot agree that the appropriate response to a mouthy teenager and some inconvenienced passengers is adult violence. If the teenager had been violent towards the conductor or other passengers first then that would be a different story but he wasn't. No violence took place until BigMan stepped in. It wasn't a violent situation until that point. The abuse to the conductor was awful but he wasn't being harmed and so waiting for the police was a better option that creating a violent situation.
You can see BigMan haul him back onto his feet on the train even though you don't see him on the floor, and this is when the seated woman with the kids pushes at BigMan to get him off her. You see the boy get back up from the platform and he's obviously been on the floor, then he tries to get back on the train (for his bag?) and is shoved to the ground again. I would call that violence if it happened to me, if someone grabbed me and dragged me and pushed me down onto the ground three times and flung their arm out into my neck to stop me getting back on the train, even if I was being a total cow, I would call it violence. My bad attitude wouldn't void their violence even if most people felt the violence was justified. It would still be violence.
I don't know how many stops there are between Edinburgh and Pol-whatsit but if the conductor didn't want to delay the train he could perhaps radio ahead to the next station and ask for the police to be waiting there for the boy.