jns - just click on the link and register with them using your credit card to pay. Then you get an access phone number and a PIN just like any other phone card but without the bit of plastic!! And if you run out of credit, you can add some more.
You can then use the hotel phone without any worries - at Disney I think you press 8 before dialing the access number and then your room bill is charged just the 75 cents for the local call.