Human Activity Recognition (HAR) that includes gait analysis may be useful for various rehabilitation and telemonitoring applications. Current gait analysis methods, such as wearables or cameras, have privacy and operational constraints, especially when used with older adults. Millimeter-Wave (MMW) radar is a promising solution for gait applications because of its low-cost, better privacy, and resilience to ambient light and climate conditions. This paper presents a novel human gait analysis method that combines the micro-Doppler spectrogram and skeletal pose estimation using MMW radar for HAR. In our approach, we used the Texas Instruments IWR6843ISK-ODS MMW radar to obtain the micro-Doppler spectrogram and point clouds for 19 human joints. We developed a multilayer Convolutional Neural Network (CNN) to recognize and classify five different gait patterns with an accuracy of 95.7 to 98.8% using MMW radar data. During training of the CNN algorithm, we used the extracted 3D coordinates of 25 joints using the Kinect V2 sensor and compared them with the point clouds data to improve the estimation. Finally, we performed a real-time simulation to observe the point cloud behavior for different activities and validated our system against the ground truth values. The proposed method demonstrates the ability to distinguish between different human activities to obtain clinically relevant gait information.