The manga/anime only derives from Donkey Kong 64 in that the settings and characters are identical to those in the game. The series also derives from Donkey Kong Country in general, including Dixie Kong as a primary character. The manga relies on story arcs continuing on a previous arc akin to Dragon Ball and Naruto, some of its humor is derived from slapstick humor and pop culture references, perhaps in order to appeal to parents who are offended by bathroom humor.
A volume usually has a plot in which the Kongs halt K. Rool and the Kremlings for a certain reason (i.e. A virus being released on DK Island and nearby worlds or a Kong being held captive in order to work a machine) and it is not uncommon for a character to interrupt the story with a humorous remark (mostly a pop culture reference or a silly story making virtually no sense at all).
Each of the manga's 20 volumes contain 13 chapters (the amount of pages often varies) and all chapters form a plot arc, a plot arc can often take up two or more volumes.