such a difficult situation this is. i know that as grown-ups, it is definitely our responsibility to make sure that all kids are safe and fine. however, it can really get difficult to understand when we really should get in the picture and when we should let it be. sometimes, yelling is still fine. however, if the parent was outright physically abusive, i would say it is important someone interferes. i once did, and even though no one else supported me, and i looked like someone who was getting into another's business, i just couldn't let the mother hit her child the way she was doing. my interfering did make her stop and go away, though i don't really know what happened afterwards.
It's pretty difficult to gauge whether or not shouting at a child would constitute abuse or not. However, if you can clearly see that the parent is shouting extremely loud, and if the kid looks like he or she is traumatized, then it's your responsibility to step in, especially since if that's what they're doing in public, you can just imagine how the parent treats the child at home. Though, you will need to know how to properly talk to the parent. You don't want the parent to be violent with you, since that would just escalate the situation.
I guess it's our social responsibility to respond to an outright abuse against other people, most especially if the person is as helpless as a kid. I haven't experienced it, though I see lots of videos of it through Facebook.