I'd say diplomacy. Russia is a powerful nation with an at least reasonably proficient secret service (the FSB might not be the match for the CIA the KGB used to be but I suppose they still know how to do their job). So, if they did try capturing him things might get messy and unlike the affairs of less powerful nations the CIA is involved in, in this case this might have serious repercussions.

Besides, what does the US stand to gain from capturing Snowden other than making an example of him? He's no immediate threat to any operations or to national security.

He is in Russia? What do you expect the FBI to do, kidnap him and smuggle him out of a country they have no jurisdiction in? Better question is why did the State Department cancel his passport on his way to Moscow knowing very well that he still could hold the key to an encrypted trove of highly sensitive documents

They could if they wanted to. Do they want to? If they get him to the U.S., they'd have to deal with him.

I don't think they want to get him because it'd dramatically limit their options and possibly set a precedent with far-reaching consequences (is he a traitor? is he a hero? what does it mean to be either? is the public ready? how well would a pardon be received? if they pardon him, who else would they have to pardon? what does it mean to leak sensitive information? what does that mean for cases of espionage?)

Why address the elephant in the room when you shouldn't have brought an elephant in the room in the first place? Just let the elephant where he is.

Personally, I have been wondering is the cozy relationship between Trump and Putin signals danger for Snowden. I could totally see Snowden being handed over as a gesture.