Where may I need Docker Compose as Kubernetes won the container orchestration war?
Docker compose is still a comparatively easy and light-weight tool to run multiple docker containers with service discovery.
Kubernetes is a metaphorical elephant.  Great if you need to smash Roman lines and win the battle, but overkill for a minor skirmish, and definitely more trouble than it's worth if you're trying to fight a small battle in the mountains.
If you have a fairly large app with multiple microservices, then Kubernetes is worth every penny.
But when you're trying to run just a couple of containers, especially if it's only on a single host (i.e. your frontend + backend and maybe a local instance of RabbitMQ), docker-compose is a much simpler/faster way to orchestrate it.  Kubernetes is like using a cannon to kill a mosquito when a flyswatter will do.
Example use cases where docker-compose works just fine:

Local development environments running on your machine.  Even if you run Kubernetes in production, there's likely a lot of orchestration around getting it to work which would make it too complex for a single machine.
Simple apps without a lot of components
Single tenant apps which run on a single host
Deploying docker-based apps on bare VMs or physical hosts