It's not just Russia; when you dabble in geopolitics, everything becomes a bargaining chip. The PR benefit of hosting Snowden is short-lived; his profile will fade over time if he keeps his mouth shut. Eventually, when Russia wants to improve relations with the US, they will likely use Snowden as a bargaining chip. He's not worth much to Russia, but the US wants him really bad. So they can use Snowden to extract something they want from the US (reduction in sanctions, for example) for relatively little cost to themselves. But there was always very little downside to Russia here, and a significant amount of upside: right now, the upside is in holding Snowden up as an example of US hypocrisy, but later that upside might be that he can be traded for something more valuable.
I'm not trying to single out Russia as a bad actor here -- the US behaved in a very similar fashion with Soviet spies and dissidents in the 70s and 80s. This is why you don't want to get involved with geopolitics - your future is controlled by situations outside your control. Snowden strikes me as a smart guy who knows all of this, which is why negotiating a return to the US makes sense for him.