>If the officer really wanted to engage with the protestors
It is painfully obvious that he did NOT want to do that. The protestors wanted to engage with him and nitpick on whatever order he had given them. They are acting hostile and trying to land the officer in question in trouble.
Yeah he kind a does it to himself by trying to play the music so the video won't end up on Youtube, but I can only see this as anti police folks having bad blood. When the protestors do anything that prevents their surveilance / recording by the police (like in Hong Kong when they were shining blinding lasers into officer's eyes and into recording equipment that was touted as genious use of technology and civil disobedience. Now that a cop tries something similar they are touted as trouble makers and assholes for simply not wanting to be recorded.
Yes it is a public place and you are allowed to record them but you don't have to bring your phone into their face.