Yes, there is evidence that looking at digital images of nature scenes can positively impact psychological and physical wellbeing. However, I cannot find any evidence relating to harder endpoints such as mortality data. Also note that there is a greater body of evidence for exposure to true nature rather than simply images or digital reconstructions of nature.
This 2011 UK review on the subject made several interesting points:
Other authors have attempted to demonstrate the human desire for connections with nature by showing test subjects photographs of urban and green environments and asking them to express their preferences for different scenes.
The presence of trees was strongly associated with feelings of relaxation. Similarly, views of gardens, flowers, and landscaped areas were highly favored.
These show simply a preference for nature images, not necessarily an improvement in health.
This study tested still and dynamic nature images against other entertainment while subjects ran on a treadmill:
Conclusions: Self-selected entertainment encouraged greater physical
performances whereas running in nature-based exercise environments
elicited greater happiness immediately after running.
This was a small study of just 30 participants, but it does show potential health benefits of nature images.
This paper (referenced in the National Geographic article) conducted an experiment by inducing stress (a simulated interview) and exploring the physiological outcomes in people recovering in two different virtual natural environments and one control group. They measured cardiovascular data and salivary cortisol.
There was prasympthetic activation (the arm of the autonomic nervous system responsible for rest and routine functions) in the group subjected to sounds of nature in a virtual natural environment. This suggests that enhanced stress recovery may occur in such surroundings.
The results demonstrate a potential mechanistic link between nature, the sounds of nature, and stress recovery, and suggest the potential importance of virtual reality as a tool in this research field.
Depledge et al. Can Natural and Virtual Environments Be Used To Promote Improved Human Health and Wellbeing? Environmental Science and Technology, 2011.
Yeh et al. Physical and Emotional Benefits of Different Exercise Environments Designed for Treadmill Running. International Journal of Environmental Research and Public Health, 2017.
Annerstedt, Währborg. Inducing physiological stress recovery with sounds of nature in a virtual reality forest — Results from a pilot study. Physiology and Behavioir, 2013.