4-player split-screen functionality was one of Minecraft 360's most highly anticipated features. Families could gather around the television and explore mysterious dungeons, or share each others' creations together. Unfortunately, for families that only own an SDTV, split-screen wasn't to become a reality. The feature only works on HDTVs, and it doesn't sound like that's going to change.
Instead, Microsoft is offering full refunds to those unaware of the situation prior to their purchase. Though if you've purchased the game recently, you'll have found the game's XBLA listing has been updated to include, "To experience split-screen functionality a high-definition television is required." Don't expect a refund if you've purchased since they've updated the listing.
However, if you did make an early purchase, and you are disappointed with said purchase, Microsoft is willing to make amends (if you're willing to put up with player support):
"We updated our pre-sale notification to inform customers that an HD screen is required for the split-screen multiplayer feature on Minecraft: Xbox 360 Edition. If a player does not have an HD screen and purchased this game prior to the notification update, they are eligible for a full refund through customer support."
Submit a ticket online, or you might have better luck giving Microsoft a call. Mention that you'd like a refund for you Minecraft purchase due to your ownership of an SD television, and then maybe try Trials: Evolution, Awesomenauts or Fez instead.
Rather unfortunate for some, I'd imagine. Though if my memory serves playing split-screen GoldenEye or Turok on an SD television was a torturous experience for my eyeballs. Save your eyes, children, and upgrade to HD! Or better yet, play Minecraft on the PC. Though, considering how fast Minecraft 360 sold, maybe you've bought both.