I recommend reading the whole article. The Wall Street Journal Law blog also highlights White's article and additional similar commentary here.
As President, Trump will appoint federal judges, from the Supreme Court to the various Courts of Appeal to the trial judges on the many District Courts. But that's not a clear or easy path to "opening up" defamation law and changing either the actual malice standard or the requirement that defamation involve false statements of fact. The Supreme Court has supported the First Amendment very strongly in the last generation, particularly in comparison with other rights. The Court has repeatedly rejected recent attempts to create new exceptions to the First Amendment or to narrow it. Consider Snyder v. Phelps, in which the Supreme Court ruled 8-1 that Westboro Baptist Church protests at funerals were protected speech. That represented a firm refutation of the notion that speech could be limited because it is hurtful or offensive. Or consider the somewhat obscure but incredibly important United States v. Stevens, in which the Court — ruling 8-1 again — overturned a federal law against "crush videos" (don't ask) and sternly rebuked the government's position that courts can create new ad hoc exceptions to the First Amendment based on a weighing of the value of speech. Or consider Reed v. Town of Gilbert last year, in which the Court unanimously (though with some justices taking a different route) held the line on the idea that laws that restrict speech based on content are subject to strict scrutiny.
I think that Trump's support for "opening up" defamation law suggests, at best, ignorance of First Amendment law and, at worst, contempt for constitutional rights. But when it comes to defamation, the First Amendment will likely emerge unscathed from Trump's presidency, though I agree with White that his brash statements about libel may embolden more litigants to file defamation lawsuits.