Mostly because it's over the internet, and the charges were for conspiracy. If any party of the conspiracy is within the jurisdiction, they can charge the whole group or any member of the group and extradite as long as there are treaties to allow it. Also, if they're facilitating a crime within the USA and/or people within the USA have access to the website, it's under Federal jurisdiction because the internet is a forum for national and international commerce. It's possible if KAT had blocked all access to North America and Hawaii, it might have avoided charges due to jurisdiction, but even then, It'd be facilitating criminal copyright infringement using a method of international commerce while harming US corporations and there's likely trade treaties with various countries to allow prosecution anyway.
He's charged with criminal copyright infringement, conspiracy to commit criminal copyright infringement, and conspiracy to commit money laundering. The first 2 have a max sentence of 5 years each, the latter has a max of 20 years. If he's lucky, he'll be allowed to plea guilty for the conspiracy to commit copyright infringement in exchange for dropping the money laundering charge, pay a huge fine and lose seized equipment and frozen bank accounts... and get a max of 5 years -- maybe as little as 1 year. That's really not bad for a 30 year old making millions a year off of a website for pirating.
The USA has its legal tendrils everywhere -- and very few countries won't extradite. Brazil and Venezuela are among a few nice places to live that refuse to extradite citizens... though, they will prosecute their citizens under their own laws if the crime is recognized there.