I was born in a communist country, you don't need to tell me. There was Labor day march elsewhere, as I wrote in the previous comment. This was a protest. They did not move and actually did call themselves a protest, not march (if you asked about that, they pointed you to the march that was elsewhere and also at another time later in the day).
All right, but I was saying so from the perspective and for the potential benefit of US readers, who celebrate Labor Day in the fall.
As for your other point, at least here in Switzerland, the delineation between "march" and "protest" is not so clear, and May Day usually features both.