I too have been trying to find a definitive answer to onboard credit and the casino for a while now and even after 20 + NCL cruises have not found one. However the following is what I have found to operate on NCL ships.
Refundable OBC is used to pay your final room account bill at the end of the cruise (just about everything you spend on board is charged to the room account), be it casino, shopping, etc’ and if there is any left over refunded.
Non Refundable credit “officially” cannot be used in the casino. It again is set against the final bill and should be used up before any refundable credit (though not for casino or service charges etc).
If you go to the casino cage and ask for cash to be charged to your room account it will be charged to your refundable OBC or credit card with the addition of a 3% fee at the end of cruise.
If you use your room card or casino card in any slot machine there is a keypad to charge your room. You just enter the last two digits of your year of birth and date and tap in the amount you want. It warns you of a 3% charge and transfers that amount to the slot machine for you to play or cash out. This charge however I have found can be paid with non refundable OBC.
So in my experience, if on the final evening of your cruise you have $100 non refundable credit left in your account and go to the casino desk and take out $100 in cash you will be billed an end of cruise £103 dollars on your credit card and lose the $100 in expired OBC.
If however you go to a slot machine and withdraw $100 which you cash out without playing and present the resulting printed slip to the same casino desk you will have $100 in your hand and be billed an end of cruise $3.