The primatologist Richard Wrangam once advanced the theory that tribe vs. tribe conspecific homicides - what he called coalitionary killing - are an evolved trait that was selected for in primates by some kind of pro-homicide selection pressures in the ancestral environment (where homicide reliably grants an advantage to the expected relative gene frequency of the perpetrator's genes). I haven't kept up with biology…
I’m trying to find the source, but I remember a primatologist claiming that humans and chimpanzees are the only two species that embark on genocide. Not being satisfied with simply defeating the enemy, but actively hunting them down to ensure they can’t harm you again. In other words, precluding retreat. (Which creates its own game-theoretical backlash: never retreat.)
In species where a prominent male has a harem of multiple females. This usually involves killing not only rival males, but all of their offspring too. Here's a Wikipedia article about it: https://en.wikipedia.org/wiki/Infanticide_(zoology)
In species which keep territories, animals will kill rivals of the same species, but because it's not targeted it's not genocidal, unless the species eusocial, in which case it can result in massive genocidal wars, e.g. https://en.wikipedia.org/w/index.php?title=War_in_ants