You can conclude that this is exactly what happened according to what evidence exactly? Who have you chosen to believe, and why?
I am piecing together a likely timeline of what happened. It is mainly from the video, what I consider normal behavior from people and from Spur's very selective statement of the event.
1) She claims that the kids arm is "so tiny" at 0:03 on the ewn video (whilst I might add quite roughly grabbing the kids arm and thrusting it up). If the kid didn't hit his kid, why would she defend such a thing? So she kinda admitted it wasn't a really big deal. Which is an inflammatory thing to say to a parent who has seen his child get hit.
2) If it were the other way around and it was him assaulting her kid (which I view as unlikely coming from a parent), she would be the one complaining at his table or it means that she doesn't really care about the kid(which I don't think is the case here). If you saw some guy grab your child and assault them, you wouldn't just sit at the table and continue as if nothing is going on.
3) Spur didn't give any indication of what occurred before he grabbed the kid. So unless there is futher information we don't have, we can assume that what he saw was his kid getting hit on the head by hers. This would be where some footage would be appreciated as it would seem this is where, whilst holding the kid, he told his kid to hit it back next time (which is terrible parenting).
4) Random people don't really film arguments unless things get heated, so we can assume the pleasantries were already passed by the time the video started recording.
5) Since she is with a number of other kids, it would most likely be reasonable to assume that she doesn't have her eyes on all of them at the same time. Which means that she might not have seen the incident at hand.
6) Every parent in the world assumes that their little flesh goblin is a complete angel, and no parent likes to have other people disciplining their child or being told that their child has no discipline. You go up to any parent and say their child is misbehaving, they will immediately assume that the person making the accusations is incorrect. Since she had numerous kids to keep an eye on, it wouldn't surprise me if she were a little stressed and annoyed. Having some Afrikaaner come up to you and state that one of the kids under her care is misbehaving was probably the last thing she needed to hear. So she probably reacted with less grace than such a situation needed. As per 1) she goes on the defensive and says it can't have been that bad.
7) This isn't good enough for the father who raises his voice and tells her again that she needs to discipline her kids.
8) She then has enough and tells him to f__k off. Which to an angry parent is pouring petrol on a fire.
After this both parties go off on a temper tantrum.
I would honestly say that both parents are equally at fault here for not de-escalating the situation, but I would say that both probably acted fairly reasonably from their points of view. Remember it is easy to judge these things as an outsider looking in, people get viciously angry when it comes to their kids and pets.
Edit.
I think 1) is incorrect. News 24 has posted an article which claims the grabbing happended at the table, which means she was entirely justified in her response.
They also state that Spur will release the footage.
http://www.news24.com/SouthAfrica/News/son-has-suffered-emotional-trauma-spur-mom-20170322