@AC 12:38 GMT - justice delayed is justice denied
I agree that you don't "understand this thing at all really".
"So it's okay if I break into your house and have a look around, as long as I don't damage anything?"
I agree that this isn't OK, and this would be a worse kind of offence than poking around in an unsecured PC with nothing of importance on it. That said, even the more serious offence you suggest in comparison probably would not justify extradition, especially if appropriate justice could be done more quickly without extradition being required.
"I don't understand this whole thing at all, really. He broke into Pentagon computers - what does he expect?"
A Pentagon or NASA computer used for highly sensitive purposes, or one used to play games in the visitor canteen ? The evidence available from both sides strongly implies something closer to the latter than the former, which makes the location of the computer irrelevant.
The point is that extradition should only ever be used for serious crimes. It should never be used for minor offences. This is because the process of taking someone away from their home and trying them in a foreign land by people with a different culture thousands of miles away from friends and family, disproportionately harms the suspect processed in this heavy handed manner.
What Gary did was wrong. But it justifies at best a non custodial sentence. Without the mitigating factors clearly evident, it would justify at worst a very short period inside in order to teach him a lesson. Dragging on extradition proceedings for a substantial fraction of Gary's life prevents him from learning from his wrongdoing and getting on with a life in which he can carry out a responsible job and pay taxes.
This is a clear case of justice delayed being justice denied.