Is Wikipedia's backwards compatibility list wrong? Should Xbox 360 be able to play Star Wars: Knights of the Old Republic?

I got an Xbox 360 specifically because I wanted to play KOTOR and my original Xbox died. I checked Wikipedia's list of original Xbox games that Xbox 360 is compatible with and saw KOTOR there so I figured I'd upgrade. (I still play mostly NES so this is a big leap for me haha.) The Xbox 360 came today, but when I put KOTOR in, it says it can't play the disc because it's not backwards compatible.

So does anyone know if Xbox 360 is really supposed to be able to play KOTOR?

Is the Wikipedia list just wrong?

https://en.wikipedia.org/wiki/List\_of\_Xbox\_games\_compatible\_with\_Xbox\_360

EDIT:

Thanks to everyone for your advice! I eventually got it to work. Being connected to the Internet alone was not enough, I needed to be logged in to an Xbox Live account.

Apparently there's a known bug that often prevents Xbox Live accounts from being created from an Xbox 360 nowadays. So that didn't work. Then when I tried creating it from my phone, it kept flagging the attempt to create an account as suspicious and refusing to create one. So that's why I didn't have it right away.

After folks here suggested logging in to Xbox Live could fix the problem, I did some more research and discovered that creating a brand new outlook email address and using that to create a new Xbox Live account can circumvent these suspicious activity flags and allow a new account to be created.

So that's what I did. After I created the new outlook email address and new Xbox Live account on my laptop, I was able to use the login information to get in on the Xbox 360, and then it finally offered to download what it needed to make KOTOR work.

Thanks again!