Previous studies have demonstrated that rhythmic training positively affects children's attention and other cognitive functions. As an engaging format, games have been widely applied in the rehabilitation of developmental disorders and cognitive enhancement. Gamified rhythmic training can increase children's motivation to participate, facilitating long-term training and effective rehabilitation. In rhythm-based games aimed at improving children's attention, assessing attention levels is critical. By measuring and evaluating attention, tasks of appropriate difficulty can be assigned to improve training effectiveness, while also validating the game's efficacy and task design. However, traditional attention assessment methods, such as questionnaires and behavioral measurements, often suffer from limited precision and complexity. These methods are more suited to screening disorders like Attention Deficit Hyperactivity Disorder (ADHD) and are not well-suited for monitoring dynamic attention in children. To address these limitations, this study introduces a non-invasive eye-tracking method, the Index of Gaze Synchronization (GSI), which quantifies children's rhythmic synchronization during gameplay by assessing the spatial and temporal synchronization rates of gaze points. The experiment involved 32 children aged 6 to 12 years who participated in six rhythmic synchronization tasks of varying difficulty. The results showed that GSI was significantly correlated with SWAN attention scale scores across different task difficulties, demonstrating that GSI effectively reflects children's attention levels in rhythm games. This suggests that GSI can serve as a reliable and valid indicator for children's attention assessment, with broad applications in both research and practice.