Hong Kong would have arrested him, but actually extraditing him would have been a process stretching out years. Releasing classified information is not an extraditable offense under the treaty, so the U.S. would have had to drum up some other charge. Snowden could have gone through several levels of appeals, each of which could have resulted in the whole thing being declared political by the courts and Snowden going free.

It could be though that the HK government preferred not to be in the middle of all this, and convinced him to leave.