You are over complicating a real world phenomenon
If they don't inherit genes, then the offspring will be rejected during pregnancy as a foreign organism no matter how much it look like a human. For example, a hyena can not breed with a dog no matter how much convergent evolution happens. But, if you flip the problem and say that they have enough common genes as humans to successfully reproduce, then no one is really going extinct because what is really happening is just the proliferation of a genetic trait. Man kind does not go extinct, we just evolve.
Genetics already has a common mechanism that will achieve more or less what you are asking for which is the "dominant trait". A dominant trait is a genetic characteristic that will replace its paired trait when both genes exist in the same organism. For example, if you have the genes for both blue and brown eyes, you will inherit brown eyes. Not bluish brown, but brown brown. This is because the gene for brown eyes is dominant to the gene for blue eyes. Likewise, let's say that humans evolve a mutation for super intelligence, and that this gene is dominant to not super intelligence, this means that everyone who inherits the gene will be super intelligent even if they also carry the stupidity gene.
Maintaining old recessive genes instead of destroying them makes a species far more resilient than getting rid of them entirely because it is very common for a gene to be superior in some contexts, and worse in others.
Your scenario could not happen naturally because it would require a ton of separate mutations, but perhaps a scientist could mess with human genetics to make a bunch of superior genes that are dominant to all genes they could replace and would spread into the rest of the population. So your "parent zero" generation would all have not 1, but many new dominant mutations.
How this would work in normal genetics is that thier children would all express the gene even if they mated with unmodified humans. Then if the hybrids mated with more unmodified humans, only some children would carry the gene; so, not all grandchildren of the super humans would have the gene at all, but some would, and they would continue to pass and spread the gene.
If your gene destroys the human gene and always inserts a double version of the gene instead of a dominate gene, you will reduce your genetic diversity which can lead to all sorts of problems.
To answer your question, natural humans may still be more selectively fit
There is no such thing as universal fitness. In the process of natural selection, it is not always better to be faster or stronger or smarter. An animal's selective fitness is all about filling whatever niche's are available, and niches can disappear.
If a new disease emerges that targets your super humans, then you could quickly go from 90% natural human replacement to only natural humans being left, but if you mix the genes normally, then maybe everyone with the super speed gene gets wiped out, but your super strength and intelligence can remain because they are not forced paired.
Another way your super human experiment might fail is that they are too well adapted to modern life. They are so good that they rapidly reproduce and overconsume resources. What you may see happen is that your new super humans progress very quickly into a period of behavioral sink or an Easter Island scenarios where your super humans outgrow thier environment faster than natural humans leading to more wars, more famines, more cannibalism, more sexual abstinence and/or homosexuality, and thier eventual extinction. Most social organisms experience behavior changes as thier group grow in size to prevent overpopulation, and if your super humans are anything like mouse experiments that have been done on this topic, they will not just self regulate into equilibrium, they will self regulate into extinction.
So, there are actually a few possible scenarios that the few remaining pockets of slow, weak, dumb humans will be the only ones left after a few centuries, and not the other way around, but if you add new genes that blend into the human race, then we will use those traits to evolve in whatever direction we need to evolve in with each subsequent generation without having to fully give up on any given option.