The rulebook says that only the planet in the home system has to be controlled to be eligible to acquire victory points from public or secret objective(s).
You've already answered your own question: You only need to control all planets in your HS in order to be eligible to qualify for VPs. The Creuss therefore do not have to control the Gate.
Note though, that the Creuss Gate system still counts as a HS in all respects, e.g. qualifying for the preliminary objectives Infiltrator or Antagonist.