It's not Kuki, it's STEM. STEM is the reading that should be used in this particular case for the kanji 茎. That's what Japanese artists like to do.
Checking wikipedia,
「茎(STEM)〜大名遊ビ編〜」(ステム だいみょうあそびへん)は、blah-blah-blah。
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The reading (in bold) is "Sutemu Daimyou Asobi Hen". There's no "Kuki" there, even though it's the dictionary reading for 茎.
Or is it read different on the album?