I suggest that using the package docker-compose-plugin would be easier than manual installing and will follow the latest standards that Docker is using with Docker Compose as a plugin. The example in the book would need to be change to remove the - but I think the execution would otherwise be the same. As of this writing the compose plug-in is v2.21.0 from the apt package. (In fact it was already installed. I assume from installing docker-ce on my PI using Docker’s instructions.)
Docker’s docker instructions
Docker’s compose instructions