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This new set of rules isn't meant to stop karaoke streams in general, it's meant to stop vtuber karaoke streams in particular. Picrel.
Hell, it's meant to stop vtubers from doing any sort of music related projects on Twitch - going by the letter of the rule, and notwithstanding the fact that Calli and Gura don't stream on Twitch, their cover of KING wouldn't be allowed on Twitch because some non-zero amount of sound (instrumentals/mixing/etc.) in the video was made by someone other than the two of them.
Theoretically, Calli wouldn't be allowed to have it on her Twitch channel because it contains Gura's vocals, and vice versa.