The parallel marker here is AND, and the word after it is 'PARTLY'. That's the parallelism. You need to have another "partly".
(A) In recent years, many prominent consumer goods retailers have increasingly invested in Mandarin-language marketing, in part that their Chinese branches should acquire new customers and partly because the Chinese Diaspora is projected to increase substantially over the next decade. - Both the "partly" issue and the "should". This isn't about what "should" happen. - Eliminate
(B) In recent years, many prominent consumer goods retailers have increasingly invested in Mandarin-language marketing, in part for the acquisition of new customers by their Chinese branches and partly because the Chinese Diaspora is projected to increase substantially over the next decade. - Both the "partly" issue and the "should". This isn't about what "should" happen. - Eliminate
(C) In recent years, many prominent consumer goods retailers have increasingly invested in Mandarin-language marketing, partly because of their Chinese branches acquiring new customers and partly because the Chinese Diaspora is projected to increase substantially over the next decade. - They don't do it "because of their Chinese branches acquiring" But they do it IN ORDER to acquire new customers for their Chinese branches. - Eliminate
(D) In recent years, many prominent consumer goods retailers have increasingly invested in Mandarin-language marketing, partly to acquire new customers for their Chinese branches and partly because the Chinese Diaspora is projected to increase substantially over the next decade. - Correct meaning and grammar, Correct
(E) In recent years, many prominent consumer goods retailers have increasingly invested in Mandarin-language marketing, partly because new customers should be acquired by their Chinese branches and partly because the Chinese Diaspora is projected to increase substantially over the next decade. - They don't do it "because of their Chinese branches acquiring" But they do it IN ORDER to acquire new customers for their Chinese branches, the "should" is still a meaning issue. - Eliminate
Ans : D