Short of that commitment, both "vertical" and "horizontal" progression are essentially just descriptions of what extra hoops you have to go through to arrive finally at decent gameplay.
Here, in XIV, it means you don't really get a fulfilling kit until around level 70, at which we arrive at our 25 or so skills (though likely inadvertantly fewer skills and therefore a higher level required with each further expansion and consequent round of job simplifications). Rather than the kit being slowed only insofar as to keep players from being overwhelmed while leveling, having that sense of "vertical" progression can require trickling out the goodies, lest the end result be too bloated or, more importantly, too much work be required.
In other, "horizontal" games, it may mean that you have 100 choices to pick from, but get only some 15 of those anyways, since it's that much harder to ensure any sort of cohesion or balance between those fractured combinations. You may get, in essence, a DRG capable of Geirskogul, Wyrmwind, Nostrand, and Mirage Dive, or a DRG capable of High Jump, Dragonfire Dive, and Starkiller, but not both. That's not always the case, mind you, but if trying to keep costs down as is done in XIV... yeah, you're probably going to be trading the actual breadth of skills you can use simultaneously (e.g., in any single span of combat) for breadth of skills that you can choose from.
An easy way to think about it is Cleric Stance before vs. healers' frequent requests for more offensive actions today. Today, if Cleric Stance were returned, many would probably hope that it takes our remaining few offensive spells off our bars and replaces them with this single button but then having that button (Cleric Stance) swap many of our healing skills over to attacks, ultimately increasing the total number of healer actions (especially, healer attacks). But, instead, it simply --in effect-- greyed out either 25% of our kit or 50% of our kit, with us merely choosing which half of our kit (after utility actions like Repose, Raise, Swiftcast, Sacred Shroud, Surecast, etc.) to be allowed access to. "Choice" only in the sense of emphasizing (and making clunkier) the choices we already had without it.
That second, lower-effort, more-constrained outcome is all too often called "horizontal progression", too, and when tacked onto an existing system, often just means that some of your skills are devalued and others overemphasized, leading to a worse gameplay experience. So, while I'd normally be all for it, I admit XIV makes me wary of how it might be added...
...On that note, any idea what you'd all want to see, or would not want to see from it?