I think it clearly would count as an arrest, which cannot take place without probable cause, a warrants, Miranda rights. At the least it violates Habeas Corpus, there were not held on a charge. Congress passed no law against recreating. The gendarmes couldn't do this to a suspect; the national park federales shouldn't be able to do it a group of innocent citizens.
I was thinking the same thing. If, say, Richard Nixon had done something similar, you would have heard the lib yowling on Mars.
Not just arrest, I would charge them individually with false imprisonment and kidnapping.