Since digital games and their scientific study are quite new, many questions concerning the fundamental nature of these phenomena remain. Two often-cited attempts to clarify the fundamental components of games include the Mechanics–Dynamics–Aesthetics Framework and the Elemental Tetrad. This theory development paper attempts to reconcile these two frameworks into a single, clear and cohesive account of the kinds of elements that constitute games. The proposed theory not only includes all of the elements from its source frameworks but also introduces two refinements: (1) it differentiates game mechanics from narrative mechanics; (2) it distinguishes three types of narratives—stories told by the developers through the game, stories that emerge from gameplay and players’ interpretations of game stories. The proposed theory should be useful for teaching game design fundamentals, as a coding scheme for qualitative data analysis and to analyse game design challenges. Subject to further clarification and extension, the proposed model may provide a basis for a general theory of digital games.