Issues running self-hosted GitLab runner (cgroups unknown)

We're trying to set-up a fully self-hosted GitLab runner that'd take care of our CI/CDs, but the build stage always fails with the following

cgroups: cgroup mountpoint does not exist: unknown

Our .gitlab-ci.yaml looks like this

image: docker:19.03.12
services:
  - docker:19.03.12-dind

stages:
  - build
  - test

variables:
  DOCKER_TLS_CERTDIR: ""
  CONTAINER_TEST_IMAGE: $CI_REGISTRY_IMAGE:$CI_COMMIT_REF_SLUG
  CONTAINER_RELEASE_IMAGE: $CI_REGISTRY_IMAGE:latest

before_script:
  - docker login -u $CI_REGISTRY_USER -p $CI_REGISTRY_PASSWORD $CI_REGISTRY

build:
  stage: build
  script:
    - docker pull $CI_REGISTRY_IMAGE:latest || true
    - docker build --cache-from $CI_REGISTRY_IMAGE:latest --tag $CI_REGISTRY_IMAGE:$CI_COMMIT_SHA --tag $CI_REGISTRY_IMAGE:latest -t $CI_REGISTRY_IMAGE ./docker/php
    - docker push $CI_REGISTRY_IMAGE:$CI_COMMIT_SHA
    - docker push $CI_REGISTRY_IMAGE:latest

test1:
  stage: test
  script:
    - docker pull $CI_REGISTRY_IMAGE:latest
    - cp .env.example .env
    - docker run --rm -v $(pwd):/var/www/html $CI_REGISTRY_IMAGE bash -c "composer install && composer ci

The runner has been set up in the same way as the tutorial on GitLab describes (The Docker version).