A pop song rendered in the style of 6 classical composers [video]
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render 1 of 2
verb
ren· der ˈren-dər
rendered; rendering ˈren-d(ə-)riŋ
transitive verb
b
(1)
: to reproduce or represent by artistic or verbal means : depict
(2)
: to give a performance of
(4)
: to execute the motions of
render a salute
c
: translateAnyway, the appropriate term would be "arranged" (or even "composed") in this context. The pieces are not improvised, so the arrangements/compositions in the given style existed before the performance.