First off, the weights that the kid is lifting are relatively light and appropriate for his age.
Second off, alot of the physical feats (handstand pushups) are actually much easier for a kid to do, because the resistance comes from your own body weight and because he has a much lighter body weight, it's actually not as hard as you'd think.
Third off, most of the things that the kid is doing is gymnastic. Children are supposed to start gymnastics at that age, because the body is still developing and it's much easier to start at age 5 rather than at age 25 when your joints are calcified.
As far as what it's doing for his body, this is what it's doing. His tendon strength, flexibility and muscular strength are increasing greatly. I'm assuming his diet is also relatively good, so basically, it's going to make him much, much healthier over all.
People have this opinion that kids can't begin learning till their teenagers. This is the exact opposite of the truth; children are actually MUCH better at learning when they're young. I wish we would start teaching nutrition and fitness at a much younger age than we do.
And lastly, at what age do you think that we start OUR kids at? I was 5 when I started ballet. My boyfriend was 7 when he started karate. If you look at most elite athlete from Wayne Gretzky to Bruce Lee, they primarily started very, very young, so their bodies would develop along with the sport.