It's a simple matter of you either disable the engines or you seize the ship, because there's no towing it out of there, there's no repairing at sea and there's no inspecting cargo while at sea
What's on video shows they attempted at seizing the ship and them targeting the engine room, you're going to have to square a circle to try to explain why they'd try to disable the ship if they had the ability to seize it, as opposed to the far more plausible explanation that they tried to seize it, failed, then targeted the engine room.
There are two obvious reasons for this contradictory approach.
The first is that this is a hatched job designed to frame China for supplying arms to Iran as a means of poisoning relations and trust between China and the other Gulf States as a desperate last ditch effort by the Americans to undo the turning of the tide and the beginning of the end of the petrodollar.
If they captured the ship, then they need to take it somewhere eventually, where the world’s media would expect to see hard, irrefutable evidence laid out for them. But if the ship’s engines are dead and it’s stuck in the middle of a war zone, all the world will get for the foreseeable future are whatever footage the American military release. Which would be hard for China to conclusively disprove. Think about it, this is an Iranian flagged ship under US sanctions. The USN could have intercepted and boarded her at any point after it left Chinese territorial waters but they only moved on it 50km from Iran’s coast?
Second, it’s a proof of concept and testing the waters of the application of domestic US shoot-first-ask-questions-later approach to law enforcement.
Rather than waste time boarding and seizing suspected blockade runners which the USN doesn’t have the numbers to do, the USN means to just shoot them, disable engines and sort it all out later, maybe.
Such a move, if applied deliberately for effect, will also leave a large number of drifting ships in the area, which could be used as cover for USN ships if they really do mean to do their amphibious assault of an Iranian island long winded suicide mission.