A business that operates in a Horizontal Market, will by definition, have a broad and diverse set of customers.
I can't find anything about it's origin on web and I guess it's just convention to call it that. A logical hypothesis could be that is based on term 'broad', when you serve a broad variety of customer, it make more sense to say you are scaling horizontally and when you are trying focus more on a segment of industry, you are scaling vertically.
Consider a company, for example a HR software company which sells a general HR platform for all types of businesses but it also have specialized HR platform specific to Law firms. If you put all the markets on a X-axis for visualization, whenever the company enhance Law firm's HR platform, it can be said it is scaling vertical and when it is trying lure/market more customers regardless of there segment, it make sense to say it's goal is to scale horizontally.