Pass variables into docker container

Problem to solve

pass variables into docker container in gitlab-ci-yml

Further details

Here is a job from my configuration (without the variables section, PROXY_HOST_NAME and BASE_DIR are empty in the docker container):

linkchecker:
    stage: linkchecker
    image:
        name: linkchecker/linkchecker
        entrypoint: [""]
    variables:
        PROXY_HOST_NAME: ${PROXY_HOST_NAME}
        BASE_DIR: ${BASE_DIR}
    script:
        - linkchecker --no-status --no-robots --no-warnings --check-extern https://${PROXY_HOST_NAME}/${BASE_DIR}/
    when: manual

How can I pass variables ${PROXY_HOST_NAME} and ${BASE_DIR} into the Docker container? In the current configuration the variables are passed on as strings:

[…]
Start checking at 2018-10-03 10:36:27+000

URL        `https://${PROXY_HOST_NAME}/${BASE_DIR}/'
Real URL   https://%24%7bproxy_host_name%7d/%24%7BBASE_DIR%7D/
Check time 0.020 seconds
Result     Error: ConnectionError: HTTPSConnectionPool(host='%24%7bproxy_host_name%7d', port=443): Max retries exceeded with url: /%24%7BBASE_DIR%7D/ (Caused by NewConnectionError('<requests.packages.urllib3.connection.VerifiedHTTPSConnection object at 0x7f5...
[…]

Proposal

Pass the value of the variables and not the name

What does success look like, and how can we measure that?

(If no way to measure success, link to an issue that will implement a way to measure this)

Links / references