Toyplay is as fuzzy term which describes the kind of play that players engage with in toys. Everything from using a toy to create something else to dolls used by children for making up stories are examples of toyplay.
Designing for toyplay is completely different to designing for gameplay or performance. Toyplay does not involve winning or a dynamic, and it tests nothing. There may be rules that govern how the toy works, but no system over and above that determines if the toy is being played with well.
Many videogames allow some aspects of toyplay. The character creation mode in a roleplaying game, which allows the player to choose appearance or gender of his avatar purely for self expression, is one example.