Barbaric literally means primitive and unsophisticated. (Sophistication referring to knowledge and culture.) When we say something is barbaric, we mean it is in its natural, unrefined, untouched-by-civilisation state.
That might make the statement "nature is barbaric" seem tautologic. But your reaction exposes its meaning. The natural state of things, the barbaric state, is on we strive to escape. It is painful and suffering. Sometimes cruel. Enough to have motivated our species to seek to not be subject to it. To be free of the "natural order of things" by developing our knowledge, culture and civilization.
As you mention, this often involved killing. But killing need not be painful and cruel.