Any XBOX 360 DVD-drive has an unique key in its firmware. If the key in the DVD-drive mismatches the key in the XBOX 360 motherboard, the XBOX 360 will recognize any game disc as a DVD-Video disc.
To resolve this issue, you need to either flash the new DVD-drive with the old DVD-drive's key (that you can extract from the old DVD-drive's firmware) or, if the DVD-drives are the same model, swap the new DVD-drive's printed circuit board with the old DVD-drive's one (the firmware is stored in a chip on the printed circuit board).
Try looking on the XBOX 360 specialized forums on how to flash your DVD-drive.
IMPORTANT NOTE: Do not discard the old DVD-drive before you extract the key from its firmware or swap the printed circuit board. There is almost impossible to extract the key from the XBOX 360 motherboard.
A.R.S., November 2012