I’m not an evolutionary biologist, but some cursory reading off wikipedia suggests that average-time-to-fixation for neutral mutations should be 4N generations, where N is effective population size. Vox’s article suggests that historical human populations were at least 55,000 individuals, which works out to ~5 million years for fixation of neutral mutations, assuming 25 years per generation.
This kind of timescale would tend to result in fixation of every neutral mutation in the population, however, not just one, and many allele differences between humans and chimpanzees were in any case not ‘neutral’- these species were obviously under powerful and divergent selection pressures, and selection can operate on standing variation in a population without necessarily having to wait for de-novo mutations to occur. Moreover, the effective human population size may only have been 3000-7500 people due to various genetic bottleneck events.