I guess it could have been faked with some kind of doll that was bait for the eagle that was swapped for a real kid while the cameraman is looking down, but that sounds pretty ridiculous and unpredictable.
The only reason not to believe it that I can see is that it's such an amazing video, but I imagine that it's ultimately just as likely that somewhere an incident like this has been caught on video than that someone would go too all the trouble of making such a convincing fake in roughly the most difficult way possible for seemingly no reason.
People have done a lot more ridiculous things to make a good youtube video and get a few oohs and ahs.
I don't see it as that unlikely that the bird is a trained falconeering bird, and the child being picked up being a doll.
In fact, I see this as extremely likely given that a bird that size shouldn't be able to lift a 7-8kg child even a foot above ground.
The running-with-the-camera is an excellent time for a switch.
I also think the child should be more injured from both the fall and the claws of the bird if it was actually attacked, and a lot more chocked.
Its not that hard to set up, no need for computer trickery, and a lot more likely then a wild big bird even being anywhere near a park with lots of people.
Bird attacks like that, even if occasionally reported, is highly debated if they actually occur at all, or is just urban legends, so if they occur they are extremely uncommon, so even less likely to get this good footage of one.