There is a 2013 documentary called A Dog's Life. It looks at how dogs perceive the world. It has been a while since I saw it, but I think that the researchers in that documentary concluded that dog vision is quite nuanced and the current theory is that is varies quite considerably between breeds. They think that some breeds are more short-sighted, while others are long-sighted. This may explain why your dog was able to see you at a distance (without waving), but struggles to see you amongst a group of people at a relatively short distance. It also tends to suggest that the render in the youtube video is at best inaccurate.
To try and resolve the issue once and for all I asked my dogs this afternoon whether they had blurred vision. They just said that they had been wondering the same about me after my shooting display the other day.
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