China? Really?
Also I'd consider that Georgia isn't a big player in the region. It's a player. But not one of the major ones. Azerbaijan is far more significant then Georgia, never mind Russia, or Turkey for that matter.
In the next decade I see Abkhazia in particular, but also S. Ossetia, strengthening ties with Russia, stabilizing internally, and slowly gaining recognition from other pro-Russian, and not terribly important countries. They will likely experience noteworthy economic growth, and S. Ossetia will continue to push for annexation by Russia. Georgia will likely face internal instability as Saakashvili and the opposition clash over just who is more anti-Russian among them. However a repeated military conflict is highly unlikely. The two regions that wanted independence the most have it, and it's guaranteed by heavy Russian military presence. Adjaria was more of a local warlords fiefdom then an ethnicity seeking independence.
The conflict that could unfreeze is the Nagorno-Karabakh conflict between Azerbaijan and Armenia. Both have been purchasing increasing quantities of Russian, and foreign, weapons, but Azerbaijan clearly has the lead, which is unsurprising, given their oil profits. However Armenia is a member of the CSTO, which means if Armenia proper is attacked, Russia and other CSTO countries will be forced to respond. And response is even more likely given the recent Russian, and Kazakh, moves to strengthen the CSTO from a loose alliance to a concrete joint military force. There is also a Russian military base in Abkhazia, which has a motor-rifles brigade, an air-defense regiment with S-300Vs, and Buks, and an air-group. Of course Azerbaijan wouldn't want Russian involvement, and counties to maintain good relations with Russia, hence why the conflict remains frozen for the time being.
Dagestan and Chechnya at this point are both pacified. The real problem is that what was a local nationalist insurgency has become a network of radical mulsim terrorist cells throughout Russia. The FSB has had very limited success in dealing with them, and terrorist attacks, as well as small groups of insurgents and bandits, continue to occur throughout the entire Russian North Caucus, rather then just Dagestan.
However the potential of these conflicts to destabilize Eurasia is close to 0. Georgia would have been the closest, had NATO been willing to take them on as a member. However saner heads prevailed, and the Europeans pretty much backed off in regards to the North Caucus, being more concerned with internal problems then with issues in a far away and impoverished region, next to Russia.
