It would also lend itself to strategy games as well. We could have a Total War style game about the Four Nations duking it out during the century prior to Aang's reemergence.
Combine with MMORPG and it's a gang war game.
Personally, I think Legend of Korra lends itself well to a sandbox action game like Infamous. Heck, even the plot of Infamous 2 has some very peculiar parallels to Book 1 of Legend of Korra. (Both Bertrand and Amon are monsters who hide of their powers from the public and seek to eradicate conduits/benders from existence.)
Republic City can work very similarly to Empire city, where you can complete side missions (taking out the bending triads and the equalist camps) to clean out the city and keep it safe to traverse. You can travel on foot, by car, leap across buildings with certain bending powers, or hitch a ride on Naga. If you step out of line or hurt civilians, there could be a notoriety meter like in Assassin's Creed or GTA that will go off, which will make Lin's Metalbenders start to chase after you.
You can have different combat combos and special moves for each of the four elements (similar to the four different weapons in God of War 3) and as you gain experience in combat, you can choose which elements you want to Level up.
So you wan't to make ATLoK game a GTA.
Strategy + MMORPG + GTA style means total gang war game.