There is indeed an arcade but you don't need quarters. You buy a card ($10 denominations I believe but I'm not sure) from either guest services or a machine in the arcade. You charge the card to your Key to World Card i.e. your shipboard account.
You can use your card or if your son has charging privileges, he can charge to his. You may want to consider whether he might charge "lots of quarters" to his card if he has the charging privileges! Not suggesting your son would do this but with my own two I have made it very clear that they can have $10 dollars worth each in the arcade but if they want any more they must ask before charging. Similarly, if they want a smoothie or soemthing along those lines they can charge it but not dozens of them for all their new friends on the ship! Otherwise charging privileges will disappear, quick smart!
By the way my son tells me that the machines in the arcade cost from 50cents to $1 each depending on the game.