Yeah, there's a Key on the PCB of your DVD drive that has to match with the key of the xbox before it will play any games. If you just swapped one in without having a matching key, it will read your game but it will treat it like a regular DVD movie disc.

The easiest thing to do if you do not want to try to retrieve your key from your current DVD drive would be to buy an identical DVD drive and just replace your old PCB into the new DVD drive, depending on your drive brand, you may or may not need to do some soldering.

If you want to try to retrive your key so that you could put that key onto a new drive, just google it or "youtube" it. There a numerous tutorials everywhere.