While I do not know for sure, I suspect the reason they didn't put winglets on the 777 had to do with the fact that it was designed to be efficient in short-haul markets as well as long haul. They increased the span instead, which nets benefits in both short and long haul, as opposed to the long haul benefits of winglets. There has been talk of adding winglets to the 777 for future aircraft designed exclusively for ultra-long haul.
As to the new super-critical wing, the 777 has it, but then, so do the A-330/340, etc., and they do have winglets as well.