The court has clear jurisdiction, actually, thanks to the Alien Tort Statute of 1789. I have no idea why this law is still on the books, though.
In fact, as the article itself says, three other circuits have agreed with the Ninth Circuit (the DC Circuit and two others, not sure which). The Second Circuit stands alone in rejecting jurisdiction on statutory grounds.
The Second and Eleventh Districts are the other two districts that have decided in favor of cases based on the ATS, for the record.
From the opinion of the 2nd District in the 1980 case of Filártiga v. Peña-Irala:
