//It is SOLELY about whether the Government is empowered to act in a matter of international relations (potentially affecting many domestic matters, such as the country's economy) without the direct authorisation of Parliament.//
If I understand the judges' summary correctly, Buenchico, it has nothing to do with the use of the Royal Prerogative (which I think means in this context the Government's acting "on the Sovereign's behalf" WITHOUT the need for Parliamentary approval) to withdraw from a treaty, nor any effects of such withdrawal. The argument seems to be that this particular treaty has resulted in the conferring of new rights on British citizens (free movement to other EU countries maybe), and that the Royal Prerogative CANNOT be used to confer or abrogate rights, such being the sole prerogative of Parliament. The Referendum Act was not mentioned in the summary (and was not used in the defence argument, for that matter), except in the observation that the act is a commitment to nothing more than organising a large opinion poll.
My interpretation may be wrong - I know nothing of law, but that's what I take the summary to mean.
As a fanatical Leaver I'm well p****d off by all this of course, but the object of my anger is not the judiciary; it's Cameron (firstly), and May (secondly). As all this must be predictable and should have been predicted May should have invoked Article 50 immediately. The summary suggests (again this is my interpretation) that A50 once invoked cannot be withdrawn. So we would have had an interesting constitutional issue on our hands: the Government has acted illegally to do something which cannot be undone.