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The whole genjutsu world was made up from scratchy ideas in Naruto's head, Dark Kurama and Menma are most likely a mental manifestation of Naruto's own dark side trying to lash out destruction.
However, the fact there is a real "dark" Kurama means that the movie producers likely had access to Kishimoto's ideas ahead of time.
Case in point, since the Genjutsu world was based on inverted personalities, that Dark Kurama could be made of Yin chakra as an inversion of real Kurama's Yang chakra.