A tournament can be called competitive and a participant can be called competitive, but these don't mean quite the same thing.
Evolution is inherently competitive, but humans become competitive by evolution.
In short? No. Fitness is.
The distinction is between competition in the sense of individuals or groups competing, over things that are often irrelevant with respect to evolution, vs the fundamental principle that given a set of environmental constraints and a limited pool of resources, an entity that can repeatedly propagate more effectively than others will tend towards a greater relative abundance.
The fact that many extremely successful species are not individually competitive proves that evolution does not require all winners to be individually competitive.