Business slang uses “vertical” to mean taking an idea to the top.
I’ve never heard that in business slang. I have heard it in air force slang to mean to rise sharply, to fly high. Literally it refers to an aircraft going straight up; only the highest performing military aircraft are capable of that. I suppose it could have transferred over to business slang, lots of military terms do, but the sense is not particular to business.
Instead, vertical in business jargon refers to a market consisting of one particular industry or demographic. A furniture company that only supplies restaurants is in a vertical market. One that sells home, office, and restaurant furniture would be in a horizontal market. Vertical media, as the author’s link points out, does the same thing. Daily Variety is a good example of vertical media, covering the entertainment industry. I used to be the news editor for the Oil Price Information Service, another example of vertical media.