This version of Donkey Kong (informally known as Donkey Kong '94, due to its 1994 release date) follows the same premise as the original game from the 1980s, in that Mario is tasked with rescuing Pauline from the eponymous Donkey Kong.
Besides adding over 90 additional stages to the original 4 stages, this release also introduces many new game-play mechanics which both help and hinder Mario from reaching his goal. Some of these new elements are patterned off concepts from other Mario games including Donkey Kong Jr., SMB, SMB 2 (USA), and SMB 3.
DrD2k9 throws barrels at DK and rescues Pauline in record time.
You can watch the complete run being played back on a console.