So, in the USA, all sidewalks are private property,...
For the most part, sidewalks in the USA are on public right of way. There are exceptions, but generally that is the case. But that does not matter in relation to police called to a scene with an unruly crowd, and particularly when violence has been reported in that crowd. In this case the police rightly act to restore order to protect public safety, which is everyone's safety. The police know walking in to the situation that they have exposure to harm, which is one reason why they wear protective gear and weapons. They are being put in harms way to keep everyone as safe as possible. This is why the public (on "public land") has an obligation to respond to reasonable instructions from law enforcement to restore order. Standing idly by pointing a video camera is pretty much a sure sign that that individual represents no threat and is not fomenting more misbehavior or getting in the way of restoring order. But obnoxiously failing to either disperse or sit down when requested to do so in this kind of circumstance is just plain stupid, and arguably an interference of a peace officer attempting to keep the peace, which is a punishable offense should an officer wish to pursue it.