Actually since he’s NOT an american citizen the first amendment doesn’t apply to him.
It applies in the sense that he cannot bring an action for liable in the United States for things printed about him in this country. When I worked for Raytheon, we had a sales representative in Brazil who made a statement about a Brazilian legislator more or less demanding "a suitcase of money". The legislator sued him in a British court! There are probably hundreds of things printed and said about him in the U.S. that would be actionable in the U.K.
Whether of not this has more to do with Sullivan v. New York Times or the First Amendment, I do not know, though Sullivan purports to be based on the Ist, there are many who believe that it is overly broad. Take the example of President Donald Trump, think of some of the non-stop slander and abuse he was routinely subjected to. Prior to Sullivan Trump would own John Brennan and MSNBC, CNN, NYT, Washington Post, etc.