What usually happens with most tire driven pirate ships, is you either have a wheel that switches direction of spin in time with the swing of the boat, to get the boat swinging. Or like
@DiogoJ42 says some pirate ships have two wheels, each spinning in a different direction. Which does the same thing, gets the ship swinging.
To stop them is the same though, you have a tire spinning in the opposite direction to the direction of travel, this brings the ride to a stop. Generally as the torque is not aggressive, the tire spinning in the opposite direction will still spin the same way as the boat, when the boat comes into contact. But there is an opposing force through the wheels. Aka the wheel wants to spin the other way, this slows the ride and gradually brings it to a stop, without wearing out the tires too quickly. The tires also raise and lower in response to the swinging.
Pulling the E-Stop cuts all power to these tires motors, and they will naturally lower so they are physically not in contact with the boat, meaning the boats take forever to come to a stop. As the boat is literally free swinging.
Funny related story. I remember the Skyflyer at Drayton Manor, having it's power cut. Which was a very similar ride to the current Pandemonium. The ride literally took 30+ minutes to come to a full stop. This also had it's motors up top. But used opposing motor power to stop the ride, like Pirate Ships do. This was after the ride's control systems failed. Including the E-stop. The ride was manually controlled with levers but it got stuck in full power and was just spinning and spinning. The operator frantically tried everything to stop it in his cab, and failed. Eventually maintenance came and pulled the rides main breakers. People were green faced to say the least when coming off, not only had they endured the ride on full power for 20 or so minutes, they then had to sit through the tedious 30 or so minutes of the ride swinging and coming to a full proper stop before it was safe to disembark. This was in the early 2000's, back way before news papers jumped onto theme parks for the slightest mishap. The ride was replaced not long after this. But it did re open a month or so later for the remainder of the season. Back then, people didn't get offended or disgusted by the slightest thing. We just got on with it. The millenials who cause all the chaos these days, were still spring chickens or not even born back then.