Normally there are more than 2 actors, which changes the reward structure.

X spends resources to kill Y. This benefits X because X doesn’t have to compete with Y anymore.

However Z also gets the benefits because they don’t have to compete with Y either. In addition Z hasn’t spent any resources to eliminate Y so Z wins. The stable equilibrium is 100% strategy Z.

Most animals will use violence in self defence, or when fighting over a specific resource. They don’t kill to remove competition.

Chimps and humans are an exception to this. Likely it’s because the coalitional nature of human and chimp violence reduces the cost of inflicting the violence to near zero, and the costs are spread across the group, so it’s worth doing.