Each player gets one of the 960 positions randomly?
No, not yet. Right now it's a tournament where Stockfish plays against itself from different starting positions — each of the 960 white setups will play against each of the 960 black setups (a full tournament will consist of 921,600 games). This is an experiment to understand which starting positions are most balanced. In about a week, online play will be available, where each player can create their own starting position (it's almost ready, just waiting for my day off).