The only problem I see is too little input.

The advantage of a neural network over a state machine or others is that it can learn, adapt, change...

For it to learn what the best approach is it has to have a lot of input for just a few outputs, so it can select the best output from all the inputs and change its output if it was a wrong decision.

What I mean is this,
When you're asked to make a decision to close your bank account you're thinking about your future, your relatives, your job and your paycheck, your cash, your investments and your own entertainment, the economy's state, the bank's state, the contract for that account and so on. All this goes into making a yes/no decision to take your money right now or leave it there.

Maybe you could add some more output for cases why you need your money there or why you need your money in your pocket, but still, the input is times more than the output, because everything affects this decision...

Same goes for your game state. Where you're looking, where the enemy is looking, was he just behind a wall or he is closing on a corner where he can hide, does he have ammo near him, does he have allies near him, are those allies behind you, and so on and so on... Its a big decision!

Good luck