Check this link:
http://www.sch.gov.qa/sch/En/catcontent.jsp?scatId=131&scatType=1
Law 20 of 2002 does not mention anything about private places such as closed areas but you definitely have the right to approach the landlord and ask him to enforce law 20 of 2002 by prohibiting smoking in children play area or even at the entrance of it.