Personally, I find myself in an odd situation.
As someone who generally is against people taking the law into their own hands, I would like to see the guy cautioned for it (or at least given a talking to about it). Indeed, following on this line I am personally quite worried about the effects of letting people take the law into their own hands. If we allow it for situations like this, then what other situations is it ok for? Who says so? What happens when people disagree with when it is appropriate or not.
However, as someone who spends an awful lot of money travelling by train, I get annoyed at those who don't pay when they should. Especially those who lie and try to argue their away around it, and especially at those who are abusive about it, and I really hope he learned something from this experience.
The point is that these low-lifes behave badly because they assume (rightly) that the rest of us will sit and watch, but not intervene. If the public was less tolerant of low-level crime it would be much less prevalent.
We are all responsible for maintaining law and order, however we normally subcontract that work to the police. In the absence of police it is our duty to do it ourselves, in the same way that it is our duty to stop at an accident if injured need our help.