In the original Mario Party roster, the playable character referred to as DK in-game is Donkey Kong.
The first Mario Party, released for the Nintendo 64, features six playable characters: Mario, Luigi, Princess Peach, Yoshi, Wario, and Donkey Kong. In the game’s character naming and gameplay presentation, Donkey Kong is abbreviated as “DK.”
Donkey Kong is part of the launch roster rather than a later addition or an unlockable character. The original game’s boards are themed around the six playable characters, so DK is also associated with one of the game’s character-themed maps.
Diddy Kong and Funky Kong are separate members of the broader Kong family and are not the character identified as DK in this roster. King K. Rool is an unrelated villain from the Donkey Kong series and was not an original Mario Party playable character.