Graph databases, such as Neo4j, play a crucial role in various applications at Gamesys, including mapping social relationships and detecting fraud. The company began using Neo4j to build a friend-of-friend referral rewards system, which helped them track fraudulent activity. They also used it to analyze quests and battles in a game centered around a fictional economy, optimizing the game's difficulty levels. This approach allowed engineers to identify and address issues more efficiently, reducing the time and effort required to balance game content.