The vote was advisory.
That means it has to be ratified by Parliament.
Those of us who made the effort to read the rules on the lid of the box before we started playing "The game of Brexit" already knew that, in principle, the vote result was not mandatory.
Democracy is a complex balance of competing needs and desires. It is an attempt to keep society stable and safe and fair. British democracy does not exist to serve "The Will of the People", it exists to give a mandate to government to rule on behalf of the people.
Governments are bound by laws and have to follow those laws, otherwise they start behaving in ways that exceed their mandate. That is, they break the democratic covenant and cease to be democratic. If May had triggered Article 50 without an Act of Parliament, she would have acted directly against the principles of our sovereign democratic government.
Personally, I don't think she ever thought she'd win the court case, and her legal advisors will have said as much. But she challange the case anyway because it was politically expedient for her to do so.
Either way, the vote was advisory. Our elected Parliament could have made the Referendum legally binding, but they chose not to do so. Our democratically elected government, with the agreement of Parliament, deliberately chose to create a Referendum that would require an Act of Parliament to leave the EU.
To now ignore the rules of our democratic system simply because the winning Brexit side doesn't like those rules would negate that initial democratic process, and would effectively be handing our country over to mob rule. The Referendum was not a vote on the right of government to break the law.
If you have a problem with the legal ruling, your argument is not with the Remainers or with the Courts, but with Cameron. He designed the Referendum - he took his democratic mandate and turned it into something divisive and poorly thought-through. But he has now left politics, so there's nothing anyone can do to lay blame where it deserves to be placed.
Ignorantia jurisdiction non excusat. Ignorance of the laws of British democracy is no excuse for breaking those laws.