Try to install plugin:
Settings -> Plugins -> Browse repositories -> type GitLab Projects Plugin minimum version 1.3.0
and go to Settings -> Other Settings -> GitLab Settings
Fill GitLab Server Url with https://gitlab.com/ (ensure slash at the end)
and
GitLab API Key with string (private token which is shown as the first thing on: https://gitlab.com/profile/account)
And then the test in IntelliJ IDEA will pass and you will be able to use ssh or https for each repository…
UPDATE: GitLab UI changed, so private tokens are created at https://gitlab.com/profile/personal_access_tokens