Let's just say that under British law, Parliament is sovereign, not "the people". And that's not even the question here. The actual matter is whether the Government (and, technically, the Queen, since she is the one in whose name the Government operates) is allowed to activate Article 50, therefore de facto nullifying the European Communities Act (an act of Parliament) without the explicit consent of Parliament. The Court ruled against that- if the Government (and therefore the Queen) wants to invalidate rights granted by an act of Parliament, she has to go to Parliament first to get its approval.
It all may sound like legalistic mumbo-jumbo dipped on a ton of legal fiction (obviously the Queen has nothing to do with any of this), but that's essentially how the British political system has worked for centuries- and that's how the people managed to drive Kings into utter political powerlessness, something that actually does matter a lot, especially since, before that, they could essentially remake law on the spot at their will. The solicitors who took this matter to court argued that giving the Government (read: Queen) the power to undo this law without the consent of Parliament would mean "undoing the result of the English civil war" that established the order of Parliament > King/Government > "the people". The court agreed.
So, in the end, the people have advised the Government in a non-binding referendum, but to make anything out of it, the Government needs to get consent from Parliament. It's that simple. It's how Parliamentary democracy works.