I don't see the difficulty. No, you don't win by giving Omega $100. Yes, it would have been a winning bet before the flip if, as you specify, the coin is fair.

The difficulty comes from projecting the ideal decision theory on people. Look how many people are ready to pay up $100, so it must be a real difficulty.

The fairness of a coin is a property of your mind, not of the coin itself. The coin can be fair in a deterministic world, the same way you can have free will in deterministic world.