Verified answer

You can only run split-screen mode on the Xbox 360 Edition of Minecraft if you are running the game in High Definition (HD) mode. This requires an HDTV. Without one, you cannot play split-screen in the game.

You can't play split-screen in Minecraft Xbox without an HDTV.

Sure that you can the only thing is you'll need an hdtv and be certain your xbox settings are set to 720 or greater an you could have the av wires switched to hd or use an hdmi cable.

I doubt it because I have a HDTV and I needed an HDMI cable; however, some -I've read- standard TVs did have an HDMI port.