Colloquial usage of the indirect object pronouns. It underlines that a person did something that affected another, from the point of view of the offended.
It's more commonly used with "me", because it's mostly my ego the one that's hurt by someone else's actions. "They did this to
me!"
Your sentence has the same meaning as: "Usó mi tarjeta de crédito para comprar(se) un aparato de sonido". ("Un equipo de música" is the same object, but in Mexico "aparato de sonido" is more common.)

He used my money to buy something without my knowledge, so this is felt like he did this to me on purpose to hurt me.
Some more examples:
- Los niños no me comen bien. -> Obviously, the children won't eat their mother, but rather they refuse to eat the food she offers them.
- Mi hijo se me casa el viernes. -> The son is getting married and the parent is sad about it.
- El perro me destruyó todas las almohadas de la casa. -> The dog destroyed the pillows, with or without an intention to be obnoxious, but I felt it as a personal offense.
- Nuestros bebés se nos fueron de la casa. -> Parents talking about their children leaving their home, obviously hurt by their action, even if it's not meant that way.