Toys and games that boys typically play: Cars, Toy guns, Cricket, Football, Hockey, Kabaddi etc.
Toys and games that girls typically play: Kitchen set, Doll, Teddy, Badminton, Skipping etc.
Reasons for the difference in the list of games:
(i) Mentality of the society.
(ii) Physical appearence of the body.
(iii) The thought that girls need to talk softly and boys need to be tough.
Yes, it does have relationship to the roles children have to play as adult as men are supposed to work outside in office and earn money while women are supposed to do household works.