In most industries, in most of the countries that produce most films, child labor is illegal. Not just highly regulated, or has special laws governing payment of the children, but illegal. Thus, in the US, I'm not allowed to hire a child to work in, say, my auto repair shop. Why is show business exempt from these laws? I tried to find some info on my own, but the only relevant stuff I was able to find was related to the payment of child actors (such as Coogan's Law http://www.sagaftra.org/content/coogan-law). In essence, I'm asking for one of two things: Either some kind of historical description of how it came about that acting was treated differently compared to other industries; or an explanation of what it is about the entertainment business in general that allows special treatment.
I would assume that the most important reason is that there isn't an alternative to child actors in movies, TV-series etc., whereas in most/all other cases the job can be executed by an adult.
Moreover not all child labor is prohibited:
These laws do not consider all work by children as child labour; exceptions include work by child artists, supervised training, certain categories of work such as those by Amish children, some forms of child work common among indigenous American children, and others.
While child acting is allowed, it is not unregulated. In the US, the activities of child actors are regulated by the governing labor union & also by federal law and state law if it exists. Longer work hours or risky stunts are prohibited in California. However to evade this filmmakers often shoots such scenes outside. Especially in California there are some of the most explicit laws protecting child actors. Being a minor, a child actor must secure an entertainment work permit before accepting any paid performing work. Compulsory education laws mandate that the education of the child actor not be disrupted while the child is working, whether the child actor is enrolled in public school, private school or even home school. The child does his/her schoolwork under the supervision of a studio teacher while on the set. Wikipedia link.
Besides all that, your main question seems to be "why acting is not considered labor for children ?" While I do not have any genuine links for information on this, we may assume that acting is not considered a very physically engaging job for children and that's why it is allowed. The other laws take care of other things, like acting doesn't hamper child's regular activities or is not too hard on him/her.
The reason why child labor was made illegal was because under-aged children were being misused into doing hard physical labor. Poverty was one of the main reasons for this. Child labor was robbing children of their education and the children were forced into it.
The difference between a child working at an auto repair workshop and a child acting in a movie/play is that the latter is creative art and does not force a child to take part in the activity of acting. Children who are actors are protected from losing education or being overworked and the content they act in is also heavily regulated.
Also, this doesn't only apply to acting, it applies to all creative arts like singing, dancing, etc.
From a simple logical view, acting is inherently different from physical labor. A undeveloped human body can easily Act without major repercussions, while physical labor can stunt growth. While the legal view of physical labor may not match the actual physiclogical consequences, acting has very minimal mental or physical consequences, and the acting that does is carefully monitored.
Simply put, Acting is no where near physical labor in terms of effect on child development.