There's nothing for them nor Russia to gain by them continuing to be this disputed territory that barely anyone in the world recognizes as a seperate state. They are basically a Russian dependency anyway, and Russia holds huge influence there.. but without the accountability and guarantee of economci development.
Annexing it would be an option, but Russia has no possible legitimate claims on it and such an action would poison relations with Georgia for a very long time, this isn't no Crimea, it has never been part of Russia, AFAIK it's always been part of Georgia to various degrees except for a couple decades in the Soviet Union before Stalin re-attached it back to Georgia.
If Russia plays it right and establishes a status as a mediator, it could secure guarantees on Georgian neutrality vis a vis NATO, negotiate it's reentrance to the CIS for starters, and the country's foreign policy vector can ultimately shift eastwards towards the Customs Union and CSTO in due course.
Unfortunately though I don't think the opposition is aiming for that. I don't think this whole crisis has much to do with Russia or Georgia really.