Interesting. I'm sort of exploring this idea in one of my projects (without Africa), and I do find it a fascinating topic.
I think that saying any one civilization will dominate is a little complicated, because after the effects of the Event will make enormous changes on the society. However [a] civilization(s) descended from African ones will probably be dominant, because they have the largest technological base at the time of the event and are the ones most poised to enter the now vacated Eurasian landmass.
There will be three (possibly four) entry points to the now vacated Eurasian landmass:
1)From Africa, across the Sahara then though either Gibraltar or the Middle East
2)From Oceana, across Indonesia (presumably New Guinea's highlands are left untouched, yes?)
3)From America across the Bering sea
(4?) It's possible, if unlikely, that Inuit may travel from Greenland to Iceland then to northern Europe.
(Note: Considering Native American watercraft technology at the time of the Event, I consider it unlikely that there will be contact between the two worlds in a reasonable timeframe)
I've made a quick sketch here:
Th red line is what (I think, I claim no expertise) will be the rough limit of Polynesian/New Guinea Highland crops in Asia, the dotted line will be the marginal (very marginal) limit. Which brings us to the next major issue, crops. The spread of civilization will be heavily limited by where crops can go. So, even though I would expect the remaining berber tribes of Africa to very rapidly spread throughout Eurasia along the deserts, subsaharan settled civilization, with cities and iron working etc. will take much lnoger since the crops won't work well north of the Sahara (it depends on if Ethiopia survives, that would change things a lot, though I'm not sure how); just look how much trouble they had in the veldt. The Polynesians have an advantage, since their crops will be more suited to more of the abandoned area (please not that I'm well aware of New Zeeland's climate, but I think the area beyond the marginal line will be too dry, not to cold, for cultivation).
These are not insurmountable challenges however, so I would expect that after a few hundreds of years, both groups will be aggressively expanding into the temperate zone, which is when things get interesting. The Subsaharan Afirecan descendnats have a large advantage due to Ironworking, but I'm not sure how long that will last. It'd be interesting to see.
So after a millenia or so, what I'd expect to see is that western Eurasia is dominated by SubSaharan African descended peoples, with East Eurasia dominated by Polynesia descendants, with somewhere around western India being the dividing line; and North Eurasia to be populated with Inuit descendants (central Asia, along the steps, by pastoral Berber descendants)
Other random notes:
-The Andean peoples will probably start to meet polynesians by the end of the first 500 years (at least). Not sure what effect that will have on Eurasia (I have a number of ideas on the Ameircas, but this post is already getting long) , but interesting.
-Most diseases will have died out, except for the in Subsahara, so that gives them another advantage.