That was not much different that a ship get leaving San Diego harbor. That said, the Persian Gulf is not San Diego Harbor, and those were American man of war ships of the line. But, who's to say that the small boats were not the Dubai yaght club?
I was in the Gulf a few times on US Naval Ships. A US Naval Ship is a government owned, American Flag ship and often in oceanographic research, maping or other activities related to navagation. Some people call them spy ships. I won't tell you that, but you can believe what you will about it.
In the Gulf, it is common to have speed boats pass close by, many times within feet of the bow of the ship. They do it to break any radar contact they might have tracking them. They do it, because they are smuggling and face extermination by 'other' naval assets from area governments, or competitors. They don't act much different that the boats I see on the cam shots of this event.
US Naval ships don't go around just blowing away speed boats. Although, it came very near this time, I suspect. Next time, I have a suspition, the little gnat speed boats will come to a hard violent end. They will deserve what they get.
Several years ago, I faced down an Iranian gun boat from my white painted US Naval Ship. All I had was a clipboard under my chin and two middle fingers held high above both sides of my head. They might have viewed me as goal posts on you favorite football field and they were read to kick a field goal as their 50 cal guns centered on my chest. I'd of shot back, but my clipboard wouldn't have sailed the 20 yards to their bridge. They turned and went away when those two US Navy jets did that supersonic flyby port and starboard of my ships stack.
Tugboat