Actually, Black begins, that is true, but the "beginning" of the game is not after choosing colors, but right at the start.
Player 1, playing Black, places his first move, white's first move, and his second move (3 stones).
Then, player 2 can either choose to:
continue the game (playing white), and then places one stone
Swap (hence the name of the SWAP2 variation) colors, and decide to be black, but since it is white's turn to play, Player1 is then next to play (a white stone)
Place two stones (white's second and black's third) and leave the color choice to the first player, who is still bl…