The City Hunter was just curious about the kid at the cemetery. He was examining him and was interested in the weapon and what the hell the kid was doing, but aside for having his laser on him he didn't have any intention of killing the kid.
You can't have the Predator spare a pregnant woman and be interested in killing a kid in the same movie. It's not out of character at all. It's completely in character for a Predator not to kill a kid because that would probably be the shittiest trophy you can get and no one would take you seriously.
Now, this scene with the Predator not killing someone because the kid is there is interesting. I wonder if it's because a kid is there, or because THIS kid is there. Maybe the kid pulled a John Conner from Terminator 2 and told the Predator killing is not OK.
But I just saw Nostalgia Critic's review of Smurfs 2 where that kid was really annoying and shitty even for a child actor.
Anyways, I predict the kid will do the clicking noise back at the Predator. I know I would.
What's a bit worrying is "nobody believes they're real", which rules out Dutch. There's a lot of people from Predator 2 who are not only aware of them, but have done some studies and gathered some data about the Predators. What happened to that?