Oh, the RFID-20 outputs at 9600 Kbps, just like NJ's uart is set up for. As a quick test, just hookup the RFID-20 to the rx pin of the launchpad (remove the rxd jumper as well), and load NJ's code, and you would get the rfid's tag id echo'd to your computer.
Your code should just go into the if received section.
if (hasReceived) // If the device has recieved a value
{
hasReceived = false; // Clear the flag
TXByte = RXByte; // Load the recieved byte into the byte to be transmitted
Transmit();