Bakspatel, I think you've got it right mostly but I've got my own theories.
Africa:
Carthage may be find itself hammered by Egypt and Morocco from east and west. Dido is a backstabber and quickly makes herself enemies. Regional powers might just grow sick of it. Rome may jump in from the north. Egypt would be content to stay small and build wonders, leaving room for Morocco to expand across the Sahara, becoming a regional power. Eventually, they'd bump into Songhai. The Zulu would have been busy swallowing up southern and central Africa. They'll probably devour Ethiopia and possibly tag team Songhai and/or Egypt with Morocco. I doubt that small civs like Ethiopia and Egypt would last long. Songhai isn't afraid to war though, so they may survive, leaving Morocco in the north, Songhai in the west and center and the Zulu in the south, east and central.
Americas:
North America: I agree with you mostly, though I think Brazil may grow strong, free to move about and build wonders unopposed with the Inca across the Andes. The Aztecs may kill of the Maya while expanding north. The Shoshone would be expanding east, north and south eventually bumping heads with the Aztecs. From my experience, the Aztecs love to war while the Shoshone are more than willing to give up their money, cities and resources after losing a few units in a war. With America and the Iroquois warring and expanding south and west and north and west respectively, the Aztecs may be free to gobble up the Shoshone as well.
Middle East:
Right on with Babylon, Assyria and Persia. I think Arabia will end up surviving, stay a small timer. Assyria will ingest Babylon while Persia profits. Their next targets could include weak and isolated Arabia, small Egypt or Byzantium/the Ottomans (Depends on if the Turks start in modern day Ankara or don't make the game at all). Assyria would certainly become a regional military and technological power. However, a determined coalition effort lead by Persia, Egypt and/or Byzantium/the Turks might put them down, after they see Assyria gobble up Arabia and Babylon.
Asia:
Mongolia will certainly fan out given all the free room, and war with any who oppose them. Korea will be squished by Chin and Japan, unless they spread out quickly to the north west. China will grow as well, perhaps killing off Korea but at the very least bumping heads with Mongolia, perhaps Siam and Japan later. Japan's isolation will prove a double edged swords, no room to expand but nice and safe. They'll have to conquer Korea to gain a foothold near the south or settle the Russian Far East. Either way, they won't get along with Korea. Indonesia's isolation and proximity to so many unoccupied islands will allow them to use their UA and grow nice and large, safely. India will also be able to grow unopposed more than likely, Persia being too preoccupied with wonders are trying to fend off Assyria. They and Siam may bump heads but I doubt they'll turn into lifelong enemies.
Europe:
Good God, what a cluster truck. Russia and the Huns have the room but the Huns aren't about to allow a competitor to exist so closely to them. Then again, Poland would be a softer target. Sweden's friendliness and room will see them become a moderate regional power. If they're smart, they'll fill the vacuum left by destroyed Russian/Hunnic cities. The Celts would be wise to overrun the English before they both en up stuck together on an island surrounded by big boys and girls. Likewise, Spain and Portugal should be at each others' throats, fighting for control over Iberia. The winner will be able to expand overseas, along with the Celts and perhaps France. Denmark and the Netherlands will be easy pickings for France and Germany, Austria and Poland will bump heads, desperate for what little room there is and Rome will march on Venice. The Greeks will explode from the Balkans, ravaging Eastern Europe, with the Ottomans/Byzantium across the Aegean, trapped between the sea and Assyria. In the end, most of if not all of the European civs would be stay small or be conquered.
I foresee...
Major powers: the Zulu, Morocco, Assyria, Indonesia, Russia, Mongolia, the Aztecs, Brazil, China.
Regional powers: Sweden, Persia, India and the Iroquois.