This is kind of a reiteration of what I wrote in an earlier log, but I feel this one more clearly describes my thoughts.
A game is made up of its rules. The pattern that is formed by these rules are what we players can feel when we consciously (or unconsciously) recognize them. To feel these rules, we'll have to interact with the game. The game then reveals bits and pieces of the rules by displaying their effects. Successfully puzzling the pieces together would probably trigger strong emotions, especially if it is something the player can identify with.
The important thing here is that the player is able to identify himself/herself with the laws of the game world. A simple way to do this is using universal themes every adult and child has experienced. E.g. love, hate, betrayal, friendship, loss, etc.
After a theme is chosen, the laws around it should be portrayed by the game. A game of friendships should explore the process of making friends and how to sustain those relationships. In this case betrayal and jealousy may also be present, but everything is supported by the overarching theme; friendship. Every child should be able to recognize the intricate act of making friends, and the pain of being left out of the game, and maybe have a faint idea about the reasons why.
With each playthrough the player would be more exposed to the consequences of the rules, and with time understand them better.
In my next log I will explore how this can more accurately be represented as a clear goal for the player.