Russia is still very active engaging in espionage in the West, just as we know the reverse is true. In that sense it is very much the way it always was, and that "Cold War" still exists.
This changes in focus and ways of how espionage in both countries is conducted. Russia does not unwittingly wish to provoke the Americans; and for what? Snowden is hardly a high target in terms of intelligence, as he was merely working for a contractor to the NSA.
Russia wins by doing nothing.
Russia stills flies nuclear bombers to the edge of US and Canada airspace. It still has agents throughout the West, many who have built lives here. The leadership in Russia is still emboldened and lauded for standing up to the US in various ways.
In many, many ways it is the same as it always was.
The only reason I think Russia might not care much about Snowden's info is the fact that Snowden got the info in the first place -- if a 6 month outside contractor had the keys to the palace, there's a good probability Russia already knows everything he knows.
Russia wins by copying his files and denying it. Espionage is alive and well, just last month a CIA officer was arrested allegedly trying to recruit agents for as much as $1 Mil a pop. The info Snowden has in his laptop is super valuable, why not have it?