In many of the web posts of this video, the 'monkey' has been described as seeing himself for the first time. Perhaps this is so, but his reaction of shock suggests that he experienced his reflection in the mirror as the very unexpected face of another baboon suddenly inches from his own face--appearing as if from nowhere. Notice how the baboon turns and looks behind himself after reflexively leaping back from the mirror. Perhaps he was looking for the other baboon who was briefly up in his face.
Can you imagine what such an experience might be like? Consider how you might react to a disembodied face suddenly appearing inches from your own and then disappearing as abruptly as it appeared. I don't know about you, but I think I would shreak like a startled baboon, if I didn't simply faint dead away.