Muscular dystrophies (MD) are a group of genetic neuromuscular disorders that cause progressive weakness and loss of muscles over time, influencing 1 in 3500 to 5000 children worldwide. New and exciting treatment options have led to a critical need for a clinical post-marketing surveillance tool to confirm the efficacy and safety of these treatments after individuals receive them in a commercial setting. For MDs, functional gait assessment is a common approach to evaluate the efficacy of the treatments because muscle weakness is reflected in individuals' walking patterns. However, there is little incentive for the family to continue to travel for such assessments due to the lack of access to specialty centers. While various existing sensing devices, such as cameras, force plates, and wearables can assess gait at home, they are limited by privacy concerns, area of coverage, and discomfort in carrying devices, which is not practical for long-term, continuous monitoring in daily settings. In this study, we introduce a novel functional gait assessment system using ambient floor vibrations, which is non-invasive and scalable, requiring only low-cost and sparsely deployed geophone sensors attached to the floor surface, suitable for in-home usage. Our system captures floor vibrations generated by footsteps from patients while they walk around and analyzes such vibrations to extract essential gait health information. To enhance interpretability and reliability under various sensing scenarios, we translate the signal patterns of floor vibration to pathological gait patterns related to MD, and develop a hierarchical learning algorithm that aggregates insights from individual footsteps to estimate a person's overall gait performance. When evaluate through real-world experiments with 36 subjects (including 15 patients with MD), our floor vibration sensing system achieves a 94.8% accuracy in predicting functional gait stages for patients with MD. Our approach enables accurate, accessible, and scalable functional gait assessment, bringing MD progressive tracking into real life.