How to configure gitlab-runner to run in the same docker host as gitlab?
Management Summary

Set the pull_policy to "never" in the [runners.docker] section by calling:

docker exec -it gitlab-runner \
  vi /etc/gitlab-runner/config.toml


Detailed Description

It seemed the problem was a confusion with images and mounted volumes.

The documentation says to configure runners in:

/etc/gitlab-runner/config.toml


Which I did, but on the host machine.
When running gitlab-runner in a docker container, it mounts a volume:

... -v /srv/gitlab-runner/config:/etc/gitlab-runner ...


This means, that the configuration file in /etc/... in the container is mounted to /srv/... on the host machine.

In this file the pull_policy was not set, which defaults to always, what ultimately caused my problem in the first place.