First, it's an obnoxiously dick move to offer it under that condition in the first place and it would never be binding-- the circumstances would change once you turn your life around and pay it back anyways-- the whole thing would just end up being reconsidered/fought over as if the money was never given to him in the first place
Second, as you said yourself, the daughter would be better off without him, and even when he comes back, he has priorities over her. So on some level, there's an "accept it for the sake of her happiness" angle to it.
Third, if it's between your daughter being out of your life for good but ultimately happy and your mother dying (basically as a direct result of your incompetence), you'd have to be a really selfish person to chose the former (and as mentioned above, that isn't even really the choice to begin with-- you can potentially fight to have your cake and eat it too).
Fourth, again, he would not be broke AND his daughter gone for good, because I'm saying that he should go to the games as part 2 of that plan. He'd be rich, his mother would be alive, he'd be able to pay back the money to the stepfather, and he'd have to uncomfortably weasel his way back into his daughter's life against the stepfather's wishes (which was the case before he took the money anyways), while genuinely presenting himself as someone that would actually be good for her instead. That's pretty good.
Really, the only thing that's at stake is whether or not he's willing to back out on his word and be on even worse terms with the stepfather by doing that, which in the grand scheme of things, isn't worth much, to be honest, and just boils down to pride.
Worst case scenario, if he dies in the games, the mother is alive and his daughter happy, which is a better situation, and if he wins the game but fails to weasel his way back into his daughter's life, his mother would be in a good spot, his daughter would be in a good spot, and he'd just have to accept it and be happy for her, which is also a better situation.