Games are complex, multi-faceted systems that share common elements and underlying narratives, such as the conflict between a hero and a big bad enemy or pursuing a goal that requires overcoming challenges. However, identifying and describing these elements together is non-trivial as they might differ in certain properties and how players might encounter the narratives. Likewise, generating narratives also pose difficulties when encoding, interpreting, and evaluating them. To address this, we present TropeTwist, a trope-based system that can describe narrative structures in games in a more abstract and generic level, allowing the definition of games' narrative structures and their generation using interconnected tropes, called narrative graphs. To demonstrate the system, we represent the narrative structure of three different games. We use MAP-Elites to generate and evaluate novel quality-diverse narrative graphs encoded as graph grammars, using these three hand-made narrative structures as targets. Both hand-made and generated narrative graphs are evaluated based on their coherence and interestingness, which are improved through evolution.