How much freedom does the player have in this type of game?

From watching these videos it seems like the player does not influence the story at all?

What if you jump into the river for example? Would you be able to swim around in it? Would bystanders be worried about you, call the police, the police would come and get you out of the water etc?

Or would a magic hand keep you from jumping into the water and you have to stay very closely on track to the scripted story?