Fitness is a conceptual assertion of procreation probability: a likelihood of an organism passing on its genetic package. Many animal species have dominance hierarchies, where breeding appears a competitive exercise. But breeding habits are much more complex. Extra-pair mating is common in many species. The nominally dominant gene package does not always carry fate within it.
Evolution is not inexorably the product of competitive selection. Instead, speciation is adaptive, not some haphazard selection process. Populations do not diverge from variation to speciation as a potential suicide pact.
Though populations face survival pressures, adaptation is not a species competition, with a winner among losers that go extinct. If that were the case, chimps and other great apes would be extinct, leaving only humans. And there would not have been several hominid species during the descent of the human races (nor multiple human races, for that matter). Contemporaneous existence of closely related species and variant populations belies the notion of competition as a primary evolutionary driver.
If evolution was competitive, adaptive niche speciation would not be ubiquitous. Instead, a few species would dominate wide swaths of ecosystems. Generalists with wide tolerances would outcompete niche specialists.
Observation of the best-known species – humans – indicates that mating selection is not entirely competitive. Breeding selection is too complex a behavior to consider fitness as anything more than an idealized concept of probability.