It's like someone being accused of murder and trying to seek asylum in another country (I'm not saying that what he did is identical to murder, just pointing out what "criminal" means here).
The concept of murder may not be as obvious as you think. If an American murder fled to Norway, he will likely not get asylum, but Norwegian authorities can't extradict him to the US, because they are not allowed to do that when there is a possibility of capital penalty. The same is the case for many other European nations.
When requesting asylum, the requester makes the claim that the charges (of whatever kind) are politically motivated - which may or may not stick in snowden's case. I have no knowledge of the history of extraditions in such matters.
He's also rolling the dice in a major way. Although the asylum laws are sort of up in the air in Hong Kong right now, they could just decide to detain him and put him in jail during the process. Worse still, since China has sovereignty, they could ship him back to China and use him as trade bait with the US.