Your dad bought the games
He used your mam's credit card
You have not given anyone, dad or mam, any money to cover the cost of the games
HOWEVER, you still feel that YOU have bought the games- even though your MAM is the one with the debt for them
YABU - you still owe for the games.
HOWEVER (and it's a big one)
However if you are seriously struggling for money your parents shouldn't be expecting gifts from you and leaving you without enough money for bills and food etc
This ^^ As a PP has said you ought not to be getting into debt if you can't manage essential bills. You say your parents know you have had to sell jewellery to pay for gifts (you get next to nowt for second-hand jewellery anyway, so that is an awful shame) - there's no way I would expect anything from my children if I knew they were strapped for cash. In fact one year my DS's birthday present to me was to come to our hime and cook us all a special birthday dinner, because he was in a position where he could just cope financially, but had nothing spare for luxuries**.
If you can afford to give them the money - give it. If you can't, apologise and say you just haven't got the cash at present. Maybe they don't realise how tight your budget is at the moment.
** It was one of my best birthday's ever!