As I understand it, the FCPA covers U.S. companies and their foreign affiliates and companies/organizations that trade securities in the U.S. If any employee or agent of such an organization bribes a foreign official, the DOJ or the SEC can go after them. "Foreign official" is defined really broadly as well. It includes foreign government employees, but also employees of international agencies and employees of government-managed industries (like doctors working for a state university hospital.) Also, the payment has to be illegal and not just "grease" money to speed up an ordinary task.
Again, I'm not a lawyer, but the DOJ might be able to draw a line from various U.S. individuals to various FIFA board members or from US Soccer to FIFA itself depending on how broad the definitions are. If they get that second one, everybody on FIFA's board is screwed.
RICO is cited in the indictment, along with wire fraud and money laundering statutes; FCPA is not.
Some combination of the Foreign Corrupt Practices Act (where a company can be prosecuted in the US for bribing officials abroad) mixed with RICO. The RICO part might not even be necessary, but it would allow them to go after anyone in the organization if they felt like it. I'm betting Blatter is sweating bullets right now.