For people stumbling onto this issue from Google.
I was using gitlab-ci-multi-runner@1.10.0 with the latest EE GDK (10.0) and running into the same 404 error
ERROR: Registering runner... failed runner=xxx status=404 Not Found
PANIC: Failed to register this runner. Perhaps you are having network problems
After some pain, I figured out the compatibility chart no longer shows gitlab-ci-multi-runner@1.10.0 compatible with GitLab 10.0. My guess is the API endpoint moved from POST /ci/api/v1/builds/register.json which seems confirmed by https://gitlab.com/gitlab-org/gitlab-ci-multi-runner/merge_requests/517
I had to update gitlab-ci-multi-runner@9.5.0, https://docs.gitlab.com/runner/install/osx.html#update