In the few Zoos around here it's pretty easy to get into almost any enclosure if you want to. In fact, they almost look exactly the same as the one in the video, with a wall that one could just climb over and, theoretically, jump down.
They usually operate on the idea that people would not be stupid enough to jump down intentionally. But of course that doesn't prevent accidents like this from happening.
I don't think it's actually known what exactly happened, but it looks like without help a small child cannot look into that enclosure, so maybe she has helped him up a bit so that he can look down and then when she didn't pay attention for a while he climbed up completely, or he himself just climbed onto that wall.
But either way, as radical as PETA usually is, the guy handling their twitter account made good points without going overboard as the rest of the internet did.