gitlab-runner exec works as its own standalone command and runs the job in the context of where the executable is called -- it will not cause the job to be run on a registered runner. It is solely a local operation, so you must have the binary available.

You can run gitlab-runner exec inside of your runner container or a new container if you want.

For example (assuming Linux platform):

docker run --rm \
       -v $(pwd):/workspace \ # mount directory to the container
       --workdir /workspace \ # set working directory
       -v /var/run/docker.sock:/var/run/docker.sock \ # enable docker
       --privileged \
       --entrypoint="gitlab-runner" \ # set entrypoint
       gitlab/gitlab-runner:latest exec docker MY_JOB

Or use doker exec to run the command on your existing container:

docker exec -it my-running-container-name gitlab-runner exec docker linting

Though, you will want to make sure the .gitlab-ci.yml file and project files are present in the container when you start it...