For such a suit to be maintained, the courts of the state where the suit is brought (the forum state) must assert jurisdiction over the defendants. This happens routinely and often. It does not require that the defendants be residents of the forum state. It merely requires that the law of the forum state allows such an assertion.
In most US states such jurisdiction is allowed if a defendant has "sufficient connection" with the forum state. Exactly what constitutes a "sufficient connection" varies, but the bar is usually fairly low. Doing remote business in the state is usually enough, and other action will suffice. In this case the plaintiff alleges that the defendant made false and defamatory statement about the plaintiff, that were published in the forum state. This is more than sufficient to support jurisdiction in any US state, and any other country that I know enough about the law of to come to a conclusion on the matter. There is no problem in bringing such a suit lawfully.
However, when a defendant is not a citizen of the same country as the forum court, there may be a problem in collecting damages, if any are awarded. The forum court probably does not have direct personal authority over the defendant. If the defendant does business in the forum, the court can seize assets to satisfy a judgement. The forum court can ask an appropriate court in the defendant's home country to enforce a judgement. Such a court may or may not do so, there is no automatic or universal rule. There may be other ways to collect on such a judgement. It depends on the specifics of the case.