[๖ۣۜℳя.๖ۣۜℳℯℴω]

If you download it from the marketplace, yes. But you can't play games from disks.
I might of misunderstood you, my bad.

Actually it does allow you to play Xbox Original games from disc. My Xbox original was broken a long time ago, and when I bought the Xbox 360 I could still play my Xbox Original games on the Xbox 360. I still have Crash Bandicoot: The Wrath of Cortex on a disc and I can still play it on the Xbox 360. I might have bought some Xbox Orignal Games on the market, but you can still play it by disc.

That's odd, because when I tried playing my old Fifa games from the original Xbox on my Xbox 360, it wouldn't read.
I tried multiple other games as well, so it wasn't the disk that was broken.

If you have the Xbox 360 Arcade it wouldn't read. If you have The Xbox Slim, Or Xbox 360 Elite. You'd be able to play it.