Since according to British law, this student has not committed any offence, should he be extradited to the US to face trial in an American court of law?
Yes - he knew exactly what he was doing - aiding and abetting people to defraud legitimate copyright holders - he made significant amounts of money doing this.
The "it's not a crime in the UK" defence just doesn't wash in this case - he defrauded people all across the world. Would you accept that someone who defrauded UK citizens should be unavailable for trial because it wasn't illegal to carry out the fraud in (say) Nevada ?
There are many faults with the UK/US extradition process - it seems very much biased against the UK and for the US - but this case is not one to make a stand on.
From The Guardian, "At its peak, TVShack was among the 1,800 most visited websites in the world, the court heard, bringing O'Dwyer advertising revenue of £15,000 per month."
I disagree with others. He set up a site that gives others the means to post illegal links. What if someone else set up a a site that encouraged users to link to gun, terrorist, drug or child porn sites. Would he have done nothing wrong then?
Giving someone the means/encouraging others, are as guilty as those that make and share the link.