This is a load of drivel. Population growth is leveling off because it takes a few generations for cultural behaviors to adapt to the fact that infant mortality magically disappeared in an evolutionary blink of an eye. Humans have plenty of genetic diversity, the critical population (the number where genetic variation increases due to random mutations faster than it is lost to inbreeding) for humans is something like 500 individuals. Even if it were a concern, we are uniquely capable to artificially increase variation through genetic engineering and selective breeding if it ever came to that. Rapid genetic collapse is simply an absurd notion. And indeed, human tool use makes us able to adapt to any other changes in our environment faster than evolution could possibly process.

At this point in time, the only thing that could wipe out humans and their descendants would be a global catastrophe comparable to previous mass extinction events where virtually everyone would be killed nearly instantaneously and any survivors could not group up to recover. Is such an event possible? Yes. Imminent? Not at all. Humans will not last forever, nothing does, but there isn't a species on earth I'd bet on to outlast us.