I think Gilbert is profoundly wrong. The key point of the vertical slice is that it tests all your real-time gameplay systems together. It gives you a sense of the player's moment-to-moment experience during a portion of the game. That requires you to prove that all your graphics, audio, gameplay, and possibly networking systems are mostly functional and integrated properly. That, in turn, is invaluable knowledge.
You always want to have a running version of your game. The vertical slice is just the first relatively complete portion you get running. Gilbert's spatial metaphor is all wrong -- from a gamer's standpoint, playing the vertical slice is like seeing a significant portion of the whole experience of the game. It's more like seeing just the Mona Lisa's face, or something. The only way this wouldn't be true is if your game consists of many tiny minigames, but even then a vertical slice (a couple of the minigames) is relevant.