They know: humans can agree on what primate gestures mean, most of the time. They don't actually know: what the primates believe the gestures mean. And: even if there is agreement, why does that say anything about our language being evolved from a common ancestor gesture language? I mean, ok that might be true, but why is this evidence for that.
Let me present my own survey data: I have deer in my yard sometimes. They know that once in a while I will throw out a couple of deadfall apples. So they ask for apples by standing, looking at me through the kitchen window for 10 minutes. Does this mean that English evolved from Deer-speak? No. The fact they're standing staring at me for a long time implies they're asking for something. Food is the only thing that fits the context. I suppose if I gave them food and they carried on staring, then I might assume they want a back rub...