The term "vertical" seems to be common amongst executives. I first came across the term when my father asked about the verticals of companies I was applying to. It appears to mean "line of business" or "field of work" or "subset of market". For example a company catering to textile industries, banks, pharmaceuticals, would have these "verticals".
So "content verticals" immediately made sense to me as "subsets of the content they produce".
PS: "we're deepening our reach into multiple markets by adding new content verticals." makes perfect sense because executives really do see the move as moving into multiple markets (or market segments) as each new magazine caters to a different class of people