Intraguild killing (such as lions killing leopards or cheetahs) has been described in multiple species.

Perhaps interesting; https://pubmed.ncbi.nlm.nih.gov/34816428/ (Still need to read it)

Cats kill things for I guess what you'd call fun, although it is food related as they hone their skills for when they may need them.

Territorial animals will kill to protect their turf. A successful species could conceivably kill off a less successful one by conquering all its territory.