Hello. Well, my English is not perfect but i will try to explain that!
First of all, there is an archaic Greek phrase "Τα παιδία παίζει". In modern times we use that phrase to describe that someone is acting like a child. It seems to me that in England you use that phrase "acting like a child" for the same reason.
This is the reason why it was written like that. However, i read the story (i don't know the film) and it means as you already said "The children don't play"! In a nutshell, the children do not have and search for a place to play.
I wish the above don't confuse you further.