You do not need to buy the Developer's Cut version of the game if you bought the PC DVD version of DKS. If you contact support with proof of purchase (either the registration key, if included, or a personalized picture of the back of the box/case, with the barcode clearly visible, and some form of personal reference on the picture), they will give you a voucher code to get the Developer's Cut version from Larian's own store. That will give you a DRM free download of the full game.
There is no way to register the retail version of DKS on Steam.