You don't have to be in competition to have an
advantage over another individual.
Advantage does not mean that one impacts the potential of
reproductive success of the other. In fact, that's largely
why there is an emphasis on survival.
You don't seem to be understanding the way NS operates
no matter how I (and others) try to explain it. It's not
about competition (although that can feature as an environmental
pressure).
Darwin does(did?) NOT require variation for natural selection,
but for evolution!! Please re-read the section that YOU
quoted to see this!
Niether did he require competition ... and as discussed before
his comment on the races of man encroaching on one another
was a dispassionate view of the way of the world, not a suggestion
that different races of man were in direct competition and that
one was better than the other.
Darwin's approach, if it lacks systemacy, was not due to arrogance,
but due to that being the way science was conducted in his day.
I don't find there to be a problem with the formal defintion
of natural selection, but I agree that many popular press
descriptions do not clearly de-couple NS from evolution.
That is understandable since NS is almost exclusively discussed
as a mechanism for driving evolution.