This paper presents a system to deliver automated and noninvasive fine motor rehabilitation through a rhythm-based game using a Leap Motion Controller. The platform is a rhythm game wherein hand gestures are used as input and must match the rhythm and gestures shown on screen, thus allowing a physical therapist to represent an exercise session as a series of patterns involving the user's hand and finger joints. Fine motor rehabilitation plays an important role in the recovery and improvement of the effects of diseases and conditions such as stroke, Parkinson's disease, multiple sclerosis, among many others. Individuals with these conditions possess a wide range of impairments such as fine motor movement. The proposed serious game is adaptive to the player to enable access to patients across a wide range of ability. In two pilot studies in collaboration with the South West Advanced Neurological Rehabilitation (SWAN Rehab) in Phoenix, Arizona, we compared the performance of individuals with fine motor impairment to individuals without impairment to determine the accessibility of the proposed serious game, i.e., to assess whether the platform is adaptive to a user's range of motion to allow an individual with fine motor impairment to perform at a similar level as a non-impaired user. We also separately evaluated the adaptive calibration algorithm to understand its impact on an individual's performance.