How do I transfer a Docker image from one machine to another one without using a repository, no matter private or public?

You will need to save the Docker image as a tar file:

docker save - o <path for generated tar file> <image name>

Then copy your image to a new system with regular file transfer tools such as cp or scp. After that you will have to load the image into Docker:

docker load -i <path to image tar file>