Avatar: The Last Airbender
You realize that the world of Avatar the Last Airbender is unusual the instant the 'inuit' girl of the Southern Water Tribe named Katara shatters an iceberg with her anger at having to wash her brother's dirty laundry. It soon becomes apparent that while she is powerful, she is no anomaly with the emergence of Aang and his 'bison' from the ice and the arrival of Zuko and his ship from the fire nation.
Between these three factions we realize that Telekinesis covers what they can do.
The Haves
The 'Benders' we learn over the course of the series are broken up into four 'elemental' manipulating factions - water, earth, fire, and air - though there are unusual groups like the sand benders (who could be earth or air benders) who seem to be borderline in their talents. Passing through each of these groups is one individual. They have their own creation myths: the earth benders learned from the badgermoles, the water benders from the push and pull of the tides and the moon, and the fire benders from the Sun. Air benders from the flying bisons.
These Benders are the ruling caste for pretty much every society except the Southern Water Tribe which has been thoroughly depopulated of its Water benders.
The Avatar
While there have always been 'benders' - the most powerful is a single entity who is reborn in a cycle taking him or her through the cycle of Air, Water, Earth, Fire for longer than anyone would care to specify. This lineage seems to go back to the beginings of this world to a point when the benders were energy benders. Its obvious that the power is 'genetic' and the Lineage of the Avatar is the source of every bender - despite their creation myths. Genetically the Avatar is the parent of all these benders - The majority of Avatars having families over the many thousands of years.
The Have Nots
Not every one had the bending ability. Katara's brother Sokka doesnt. Though this may be either through loss of the southern water tribe benders able to teach them as children, because Sokka's Chakkra's are blocked - Fear being a psycological padlock on the mind (likely a result of the death of his mother during his childhood), or genetic chance. In a world ruled by benders the have nots are considered permanently disadvantaged peasants by those who have the power.
There are non-benders who dont see it that way:
The Chi Blockers have the ability to attack key points on the physical body of a bender and simply take their powers away and leave their bodies paralyzed.
The Kyoshi Warriors - women trained in martial arts by Avatar would be another warrior caste standing against the benders where possible.
In the end you percieve The Lineage to be at the centre of it all. A bloodline from which all telekinetics in this 'world' are descended.
How Technology rose and fell with the Tide
Watching the series you realize that bending has shut down technology. While the Fire nation seems the most advanced - making use of it in the hundred years war it has been running for the last century, this is an aberation. Technology is kept low and thus when it is available it is to the elite few. The childhood toys of the Avatar have amongst their collection what looks like a basis of a helicopter. Machines such as warships, dirigables, submarines, vehicles, and technologies such as siege engines and explosives are all available to those who will develop them but they exist at the whim of the Benders.
What we see is that technology seems to rise and fall with the emergence and fall of tyrants willing to make use of it or control it. Even the Avatar is instrumental in technological and multicultural repression.
The Wildlife is a tidal wave of Genetic Aberations
The natural world is dominated by weird animals like a Gargantuan sentient Lion Turtle, Penguin-seals, Flying bison, Flying Lemur, Platapus Bears, Koala Otters, and livestock like Riding Birds, and food animals like Pig-Chickens, Sheep-Pigs, and Cow-pigs. So our world is one of genetic modification where an actual Bear named Bosco in the hands of the Earth King of Ba-Sing-Sei is exotic and a one-off.
The Geography is no longer like the Earth we know
The world is changed. The map tells us it is as big as Earth but the Geography is altered. Land exists at the North and South Pole. In a world where every Avatar had the ability to raise an island or sink or divide a continent with telekinetic power is it any wonder.
The world of the Avatar is half the planet. The other half simply isnt known. Where did the Airbenders Go if they didnt go extinct? If half the world is beyond the Rule of the Avatar, it is there that they might hide.
Religion: Where did God Go?
While Religion as we have known it fell by the wayside - the Avatar - despite the fact he is as human as the rest has access to a superconciousness state known as the Avatar State. This is as much a God like figure as anything. There are temples in each of these regions devoted to the Avatar - and the Priest class associated with these temples have struggled to build a religion in which they have power from the Avatar. That the Avatar has a wife or husband and children seems to be the big muddy secret that is kept by the priests from even the ordinary benders. The Idea that there is a Lineage from which all benders are the descendants of the Avatars is a church secret.
A World of Ruins
There are ruins everywhere. Aang, Sokka, and Katara take shelter in a ruined citadel after Sokka falls ill - followed by Katara. In Book of Earth there is a library in the desert filled with as much knowledge as the Avatar Temples seem filled with Avatar generations. Appa the flying bison shelters in a rock shelter that is overgrown by centuries of forest during 'Appa's lost days'. Civilizations have risen and fallen and vanished.
A Scifi tale?
Yes. It has all the aspects of one. A world so far in the future it has changed. A World of Genetic Aberations, Telekinetics, built on the remains of our humanity.
Addendum: The end of Legend of Korra
With multicultural humanity now huddled in Republic City, where technology is advancing somewhat, we can only watch the human conflict as the rising technology of the Earth Kingdom under Kuvira meets the power of the Avatar, and bam! The power of the spirit vines harnessed to power earth kingdom mecha ends in an unleashed nuclear blast that, though we are not told, has killed everyone in Republic City. Avatar Korra begins leading the dead into the Spirit World. The Avatar has once again been instrumental in the elimination multiculturalism and Technology.
