Δ Model of engagement
Engagement is an active loop of participation, or conversation with a medium. Games are inherently engaging mediums because they create create active participation. Conversely books and television tend to be primarily immersive mediums (Immersive mediums replace thought) which do not require active participation.
A framework for structuring thought is also a framework for asking good questions, so to create a model for thinking about what makes something engaging would help to ask deeper questions about how we interact with different mediums and how new mediums can be created and evolve to foster more active participation.
My personal model for engagement involves Three engagement factors: goal, space, and tools. At least two of these engagement factors must be present simultaneously to create an engaging experience; and each pair comes together to form the Three approaches to engagement: puzzle, exploration, and curiosity.