Human action recognition is a challenging problem, particularly when there is high variability in factors such as subject appearance, backgrounds and viewpoint. While deep neural networks (DNNs) have been shown to perform well on action recognition tasks, they typically require large amounts of high-quality labeled data to achieve robust performance across a variety of conditions. Synthetic data has shown promise as a way to avoid the substantial costs and potential ethical concerns associated with collecting and labeling enormous amounts of data in the real-world. However, synthetic data may differ from real data in important ways. This phenomenon, known as domain shift, can limit the utility of synthetic data in robotics applications. To mitigate the effects of domain shift, substantial effort is being dedicated to the development of domain adaptation (DA) techniques. Yet, much remains to be understood about how best to develop these techniques. In this paper, we introduce a new dataset called Robot Control Gestures (RoCoG-v2). The dataset is composed of both real and synthetic videos from seven gesture classes, and is intended to support the study of synthetic-to-real domain shift for video action recognition. Our work expands upon existing datasets by focusing the action classes on gestures for human-robot teaming, as well as by enabling investigation of domain shift in both ground and aerial views. We present baseline results using state-of-the-art action recognition and domain adaptation algorithms and offer initial insight on tackling the synthetic-to-real and ground-to-air domain shifts. Instructions on accessing the dataset can be found at https://github.com/reddyav1/RoCoG-v2.