I understand but at the same time, it's a bit vague because Digital media can be used to mention simply digital content. I cannot say with absolute certainty and I might be mistaken here but I don't think we can say that the New York times is a digital media but we can say it's a digital media company. By saying a digital media company we can remove the ambiguity. Also, I understand I might be getting very pedantic here.
I cannot seem to negate Option D as wrong either, though you are right that the sentence might be conveying or intending to convey Digital media companies' emphasis on promotion expense. To me, "Digital media studies of promotion expenses" makes more sense than "In studying promotion expenses, the digital media". The later part of Option D "Digital media studies of promotion expenses
have had as an emphasis" might be wrong because of idiom usage but I am not sure, I'll need to check the idiom usage of emphasis I guess.
Overall, I guess the answer option is a bit shaky but we have to select the correct one among 5, not the best one out there.