Human gait analysis has been one of the primary procedures for diagnosis in modern healthcare applications for various diseases. Instead of using expensive wearable sensors on patients, this research aims to assist in gait analysis and classification for medical diagnoses using computer vision solely. A long short-term memory (LSTM) neural network based on MediaPipe Pose for video-based human gait analysis is proposed to assist in diagnosing patients with neurodegenerative diseases, particularly cerebellar ataxia. The kinematic parameters were extracted from the pose estimation model on captured gait videos before deriving the spatiotemporal parameters for quantitative gait analysis. Data augmentation is applied to increase dataset size, and five-fold cross-validation is performed to verify the suitability of the developed dataset for training deep neural networks. The selected LSTM model achieves a testing accuracy of 99.8% with very high precision and recall metrics for ataxic and normal gait classes. The proposed methodology can be applied in broader applications for remote rehabilitation and patient monitoring.