I haven't heard it related to data science.
But it may mean text analysis like Coleman Liau, Flesch Kincaid, Dale-Chall, SMOG
These were invented to assess readability of a given long written text considering average sentence length, paragraph length, use of polysyllabic words, simple/complex words, passive voice and other guidance an english professor might give. Over time, though, they have been used to compare multiple texts for shared style. Imagine a formula that assigns a probability of plagiarism in a new essay based on an individuals previous writing.
Again, thats a guess. Never heard it called Quantitative Content Analysis or seen it applied outside the writing community.