So the whole TV series was called the "Game of Thrones", implying that there was a game.
The name "Game of Thrones" was not chosen to describe the whole show's story as one "game".
The show was named after the first book in the series of novels it is based on, "A Game Of Thrones", which corresponds to the first series of the TV show, in which Ned Stark was dumped into a deadly political game he didn't understand. That's the game that the titular phrase "Game of Thrones" was coined for: the game where Ned reluctantly played, lost, and died.
You can argue that there are more games of thrones throughout the series, but the name "Game of Thrones" was not chosen with those in mind, and the show-runners couldn't have had the series's eventual ending in mind at the point the show was named.
The title of the show was therefore not chosen as a pointer as to how the ending was intended to be interpreted.
In various interviews, the show-runners discuss that:
- They chose the name of the first book, rather than the name of the series ("A Song Of Fire And Ice"), because it was more accessible to non-fantasy fans. Their initial pitch for the show was "The Sopranos in Middle Earth" and they wanted the broadest possible appeal.
- At first, they weren't expecting to necessarily succeed in getting funding to film the entire series, including books that hadn't (and still haven't) been written - they have said that one of their main goals initially was to do well enough commercially to be able to reach a third season and film the "Red Wedding" scene [I can't find the interview where they said this at the moment].
Did Brandon Stark win the "Game of Thrones"?
This is subjective. You can argue he did by becoming king, or you can argue that nobody did, because the throne was destroyed, or because the nature of the game was changed by Bran's election, etc etc.
