The operation of telerobotic systems can be a challenging task, requiring intuitive and efficient interfaces to enable inexperienced users to attain a high level of proficiency. Body-Machine Interfaces (BoMI) represent a promising alternative to standard control devices, such as joysticks, because they leverage intuitive body motion and gestures. It has been shown that the use of Virtual Reality (VR) and first-person view perspectives can increase the user's sense of presence in avatars. However, it is unclear if these beneficial effects occur also in the teleoperation of non-anthropomorphic robots that display motion patterns different from those of humans. Here we describe experimental results on teleoperation of a non-anthropomorphic drone showing that VR correlates with a higher sense of spatial presence, whereas viewpoints moving coherently with the robot are associated with a higher sense of embodiment. Furthermore, the experimental results show that spontaneous body motion patterns are affected by VR and viewpoint conditions in terms of variability, amplitude, and robot correlates, suggesting that the design of BoMIs for drone teleoperation must take into account the use of Virtual Reality and the choice of the viewpoint.