Both eyes open is great for the real world. Olympic target shooting is a very different animal. Don’t think of it like normal shooting. Situational awareness is not a factor. Unlike practical shooting, tunnel vision is desired. Most shooters wear blinders to obscure the off side eye. On the aiming eye they often wear special glasses. They are focusing on absolutely lining up the physical sights, there are no optics in Olympic pistol shooting.
For comparison, this is what a more conventional Olympic headgear setup looks like.
Yes the hand in pocket is pretty common in Olympic shooting. Unfortunate that it was part of the list as it undercuts the rest of the valid observations unusualness of the setup and success.
This shooter was much more casual than most. Most shooters will line up with special highly stable, but strange looking stances.