what does the Docker Engine even do?

The Docker Engine as a clients-server applications. It is made up of three components:

dockerd

- Dockerd is a server with a long running daemon process that is used to manage containers

docker engine APIs

- This api provides a way to interact with the Docker daemon. The docker engine API specifies the interfaces that programs can use to talk to and instruct the Dockker daemon

docker cli

- Command Like Interface(CLI) that leverages the docker engine's APIs to interact with the the daemon(dockerd)