Weapon (d4)

In my opinion, this reconstruction isn't "true." It mainly consists of just one battle and has a straightforward plot, denying the freedom of choice, as in RPGs.

You don't know much about them. Reconstruction isn't just about battles.
I spent a year in their community. They teach history there, sew costumes, make household items, and for the third year, they are planning to organize historical fencing.
Well, some good reenactors do organize them, but the point isn't in fencing; reconstruction != battle.
And yes, there are blacksmiths. We didn't have a fire because there's no forge in the city. I made chainmail rings and cleaned armor.
And, of course, there are good reenactors and bad reenactors, good role-players and bad role-players.
In general, role-players appeal to me more because I like fantasy more than real-life history.

Added after 3 minutes
And Tolkienists are just role-players, but within the Tolkien universe.
And again, role-playing != battle. It's directly about playing a role. It doesn't necessarily have to be expressed in combat.
But role-playing is always some kind of game.
Your conclusion, because role-playing = role-playing game