So the phrase refers really to a fitness of a line of generations. An individual's length of life may tend to increase or decrease the number of offspring that an individual reproduces. Differential mortality impacts differential fertility. But the critical difference in "fitness" of individuals is differential fertility. Perhaps this is the individual "fitness" you refer to. It still seems that this must be measured at a group level ( either species ;or breed or type , a group at the sub-species level all of the same species).
Fitness would refer to the differential fitness between two breeds or groups, A and B. Group A has a trait or traits. Group B has a different trait or traits from Group A; If the traits of Group A enhance the fitness over Group B , then Group A's fitness is higher. Not all breeds would necessarily have different fitnesses.
I can see that Darwin might refer to "species" in the title, but mean both species and breed under the later 1940's definition of "species" , i.e. ability of two individuals of the opposite sex to mate and produce viable and fertile offspring. Two breeds are of the same species, but with some salient( or highlighted for a given purpose )characteristics that are different.
The examples of modern experiments demonstrating different fitnesses of populations of organisms are different breed populations , such as the moths that change from dark colored to light colored or vica versa because of the change in which color functions as camouflage when industrial smoke changes their environment; or bacteria developing breeds that are immune to antibiotics.
Mass extinction and replacement by new species
The popularly famous example is dinosaurs: many different species dying off in a natural historically relatively short time frame. They are replaced by mammalian species which had been relatively small in size ( and maybe number) . With many ecological niches vacated by dinosaurs, and perhaps many predators species gone , mammals "radiate" out into the vacant niches. They separate geographically. New species originate. Here the main "fitness" was surviving the mass die off of dinosaurs, assuming it was caused by a famine because of a comet crash destroying much plant life and animal life directly. The smallness in size of the mammals may have bestowed greater fitness than dinosaurs in the drastically changed environment.