I always interpreted the "survival of the fittest" as inherent to one single species.
For a given species, only the fittest individuals survive and reproduce, thus spreading the fitness genes.
If no fit individuals exist for any given species, it becomes extinct.
Here, "fit" can be quite broad.
For example, you can cross a male donkey and a female horse, you have some chances of getting a mule. This is a hybrid species, not horse, nor donkey. However, it is not fit to propagate its genes.
For a given species, only the fittest individuals survive and reproduce, thus spreading the fitness genes.
If no fit individuals exist for any given species, it becomes extinct.
Here, "fit" can be quite broad.
For example, you can cross a male donkey and a female horse, you have some chances of getting a mule. This is a hybrid species, not horse, nor donkey. However, it is not fit to propagate its genes.