This is really an argument using teleology to derive an ought from an is. It is similar to the statement that one "ought" not to sacrifice one's queen during the first few moves of a game of Chess, which attempts to bridge the is-ought gap by assuming that the goal of playing Chess is to win.
Here, the teleological assumption is that biological life has a purpose, and that purpose is to reproduce. Once you accept that, it follows that one ought not to do things which are reproductively unsustainable. It's not hard to imagine that actions such as murder could fall into that category by undermining social cohesion.
It is a case of seeing repeated behaviour (of microbes, plants and jellyfish, reproducing) and inferring that the behaviour must have a goal. It is not so different from Paley seeing complexity and inferring that there must be design. But one can release a ball from a balcony and every time it will fall towards the ground, yet that does not mean that the purpose of balls is to fall downward.
Effectively, it is trying to derive morality from a command to "Go forth and be fruitful", and saying that the command comes not from a Middle Eastern deity but from something called "nature" or "evolution". Either way it's still possible to consider that it's a command which has not been fully justified or lacks authority. Many people think nature is mindless and has no intention, but some people might think nature is actually evil and should be disobeyed.
At best, this gives us a naturalistic justification for human societies to label murder as wrong, something to be discouraged and sanctioned. Maybe hunter-gatherer groups which failed todid not consider murder blame-worthy tended to go extinct? But you can't derive rightness or wrongness from survivor bias. After all, naturalistically speaking there is no right or wrong when species fail to reproduce or go extinct, it has been very common as long as there has been life on Earth.