I could very well be missing some aspect, but I'm not really seeing the added challenge here. Tic Tac Toe is easily solved, and playing this game by selecting the optimal 2 moves in regular Tic Tac Toe seems to be the best (and obvious?) strategy, which means that the entire game just comes down to who wins the critical coin toss.
I don't actually see where there's any strategic decision to be made but if I'm wrong about this I'd love for someone to point it out.
The motivation for the game as listed on the page, was to make the original tic-tac-toe (a timepass game), slightly interesting.
The coin toss forces the suboptimal move, thereby giving the other player a chance to play the optimal move next time. The original game is quite easy, and becomes boring because most games tend to be tied. This configurations will allow individuals to keep playing, for a longer duration, knowing that the other player might not be able to play the most optimal move.
I don't actually see where there's any strategic decision to be made but if I'm wrong about this I'd love for someone to point it out.