You used tendencies to justify the nonexistence of alternate responses/temperament from people who do not seek competition, and cited universal human experience as support. The bit where you connected those descriptors to the non-competitive person is where I take issue, though I do agree on one which is that to some degree everyone cares about winning.The first two and the last I described as tendencies, not rules. It is certainly not the courageous person who is a scrub, it is the coward. Hence there is a relationship, and a tendency there.
Aggression is inherent in all human activity. Picking up a cup is an aggressive act. Suppressing desire is an aggressive act, etc. All effects require force, and all forceful acts are acts of aggression. That is how I use the term.
So, again, no assumptions are made.
Aggression is definitely not the right term for what you are describing. Maybe agency or action. Aggression has a bit more valence to it, but I feel you on that point.