A lot of animals have had severe bottlenecks like that in the past. Cheetahs, for example, have so very little genetic diversity that they're all essentially cousins; cheetahs will accept skin grafts from any other cheetah with no fear of rejection. Humans have also had a pretty extreme bottleneck in our history, with estimates that there were no more than about a thousand alive at one point, which is why we don't have the diversity many other animals have. If we manage the remaining population carefully, even a small population can rebound with few fears of later genetic problems.
Nitpick: a historical population bottleneck does not necessarily mean that only that many individuals were left alive at a single time; it only means that that many individuals from a single time successfully contributed to today's population.
Simple example: imagine you have two groups of humans, A and B, living in two neighboring valleys. Group A consists of 1000 individuals, group B a million. Over the next several hundred or thousand years, group A thrives and slowly increases to a million people. Meanwhile, group B declines to extinction at an even pace.
At no time were there fewer than a million people, but there was a population bottleneck of 1000 people.
In that scenario you could make a pretty good argument that group B were not modern humans but instead a dead race. (Assuming they had all these unique genes that disappeared.)
I'm not sure the nitpick makes things more accurate.
"Race" is not really a recognized concept outside of social interaction. I believe "sub-species" is preferred on the level that you're indicating—think neanderthals and denisovans. Even then, it's a measure of phylogenetic distance, not of any quality that directly "matters" (like fertility of offspring).
Anyway, they're all humans in terms of having active sex with humans.
I don't understand where you're going with this in relation to saalweachter's imaginary groups A and B. Neanderthal genes have nothing to do with population bottlenecks.
If you want to get more complex, you could assume that group A was a colony from group B and that they were a genetic subset of group B.
It's also possible that group A and group B were still economically linked, with frequent trade between the two but no intermarriage.
It's also possible that group A and group B were never at any time distinct groups, and the individuals who 'won' genetically were scattered through time and space among a larger population. Imagine a rare mutation that confers an immunity to a terrible disease which periodically ravages the population. It's not that the plague kills off all but 1000 people, it's that over centuries of large numbers of people being killed off, those descending from the few people with the mutation (and their mates) come to dominate the gene pool, even if there were always millions of survivors.
The reason for the nitpick is that the idea of a human population bottleneck is almost-always interpreted as "humans almost went extinct!". Maybe that happens to be the case, but it isn't necessarily so.
In that scenario, with lots of gene mixing going on, there isn't really a cutback of genes at any point. There is only a requirement that those thousand people are somewhere in everyone's ancestry. This is very different from them being the only ancestry. The useful gene spreads throughout the population with no bottleneck. No genetic variety goes away except in the case that it's specifically incompatible with the anti-plague gene.
Even without die-offs, you approach a situation where everyone shares all (millions) of their ancestors at some depth. Having a particular thousand somewhere in a logistically-growing list is not the same as domination.
