The point behind that condition is to let the system have a better idea of what your rating is. When your games are "unrated," as three of yours were, then the system hasn't had sufficient opportunity to properly rate you.
True, the message you had says nothing about them needing to be rated games, but it should. Unfortunately, this means you still need to complete three more rated Online Chess games to be able to join a tournament.
I have completed exactly 5 online chess games as of 5 minutes ago, and I would like to join a tournament, but when I click join, a message which says "You must have completed at least 5 "Online Chess" games to compete in this tournament." Appears. I'd really like to join a tournament. Please help!