Nowadays, stroke is one of the leading causes of death and disability. Consequently, post-stroke hand rehabilitation is essential for patients to recover their hand functions. However, traditional approaches to hand rehabilitation usually involve repetitive hand exercises, which can be tedious and not engaging, leading to poor adherence of patients to the treatment plan. Recently, game-based approaches have been widely adopted to make hand rehabilitation more interactive and enjoyable. Game-based systems create an interactive environment where patients can enjoy the games while still participating in the recovery process, thus enhancing the interest and engagement of patients. Moreover, the significant growth of Artificial Intelligence and Computer Vision has led to the development of advanced hand gesture recognition techniques that could be applied in game-based systems and achieve high accuracy. This work proposes a real-time hand gesture recognition system and a gaming application for hand rehabilitation. The purpose of this work is to support and encourage patients to practice hand therapy exercises by means of interesting video games. The proposed system can recognize predefined hand gestures using the skeletal data captured by a Leap Motion Controller and then use the gestures to interact with the game environment. All the hand gestures were selected from common hand and wrist therapy exercises that are often practiced by post-stroke patients. We also conducted a user study involving 10 participants from different demographic backgrounds to evaluate the effectiveness of the system. The results showed that the proposed system is engaging and can be a potential solution to hand rehabilitation.