The COVID-19 pandemic has suspended physical classes and influenced students from underprivileged groups more seriously due to their poor living conditions and digital disadvantages. To understand the impact of the constrained learning, we conducted a study on game-based learning to examine the effectiveness of computer-aided and autonomous learning of traditional Chinese by underprivileged students. From December 2020 to May 2021, we collected 3245 quiz results from 26 underprivileged students over six months. The quizzes systematically covered the fundamentals of learning traditional Chinese in six aspects, i.e., literacy, orthography, phonology, morphology, speaking, and writing. We analyzed the results to understand the learning efficacy of students. Remarkably, students can significantly improve their skills in literacy and phonology through unsupervised game-based learning. Furthermore, by parsing the writing tasks, we observe substantial improvements among 7 out of 13 common types of writing mistakes. Our study provides a critical lens to understand the design opportunities of game-based learning without direct supervision.