Self-awareness in humans and mammals: predators and prey

I just read Richard Leakey's 1992 book, Origins Reconsidered. He talks about self-awareness as being one of the hall-marks of human cognition, and it’s demonstrated by deception—if you can think to deceive someone, you must be able to imagine what he/she is thinking and how he/she will react to your own actions. The development of this went along with transitioning to a hunter-gatherer society. I remembered hunting (formerly with a rifle, now with a camera) and recalled how every hunter, when in sight of the quarry, will look away and pretend not to notice the quarry, while working closer enough for a shot. Especially, we never make eye contact with our prey. This is universal hunting behaviour. It seems innate: so obvious that it doesn’t have to be taught. Then I thought, wait a minute: the prey must have some self-awareness to observe the hunter and decide whether its intentions are dangerous or not.
One can extend this in many directions, e.g.: (1) On my morning walks, when I pass a house with a dog on the porch, if I don’t seem to notice it, it watches me casually, briefly, and then looks away. But if I stop and look directly at it, first I see the hackles rise, and within a second or two it’s on its feet in an agonistic posture, or barking. (2) I have a photo of 27 mature bighorn sheep rams sunning in a steep meadow and not one is looking directly at any of the others. I had read Val Geist’s book and easily recognized this confrontation-avoidance tactic. (3) Sheep “present horns” to each other during male-male competitions: one stands broadside and holds his head so his opponent can see the size of his curl. Once when I came upon a Dall sheep ram in the Yukon, at first I looked studiously away and pretended not to notice him, so I could get closer for a photo. But the terrain prevented a close approach, so I made myself into a threatening ram by holding my arm up beside my head in a curl, broadside to the ram, and he instantly reacted assertively, strutting back and forth presenting me his horns, and coming closer and closer until I decided that was close enough and took the photo—whereupon he went back to grazing. So in this case, I was humanly deceiving him and he was bovinely reacting, but he must have had some sort of self-awareness to determine my changing states of attention (and intention) towards him.
How many wildlife films have we seen of a wolf among caribou, or a lion among wildebeest, pretending to ignore them while the prey watch intently to try to determine their intentions? Are these hunters not practicing deception?
Probably Leaky could explain this, but didn’t go into the nuances because of space limitation, and to not bore his audience. When I get a minute, I'll look into the literature.