Executive Summary: Yahtzee has rediscovered the old-school definition of replay-value as a quality of a game that manifests from the game providing an experiential state that one immerses oneself into repeatedly for the pure pleasure of being in that state, not from forced repetition for the completion of achievements, tasks, or goals.
And now the wall-of-text:
Sounds to me like Yahtzee has rediscovered the old-school definition of replay-value and has rejected the new-school definition of replay-value. As an old-schooler myself, the understanding that I have of replay-value is that quality of the game that entices you to play the game again, possibly multiple times, purely for the sheer pleasurable enjoyment of experiencing the game again. However, these days, replay-value seems to be defined by the number of chores the game gives you to force you to repeatedly play the game again for the sake of completing the chores--i.e. achievement grinding, loot grinding, character configuration grinding, branching quests grinding, scenario grinding (see a pattern, yet?), ending grinding, etc. grinding. The failure of the new-school games in creating true replay-value is that they are not designed as experiences but rather as a compilation of "stuff to do". They're not actual works of holistic, experiential gaming; they're just busy-centers, like the Child's Busy-Center you buy for infants. They're a bunch of events, quests, toDos, and goings-on that aren't always properly engineered to seamlessly blend together into a self-consistent, coherent and holistic experience for the gamer, and this, in my opinion, is the critical separation of the old-school view from the new-school view of replay-value.
But, why has this new-school definition of replay-value come about? My guess is that it developed because, back in the day, people wanted a more quantifiable definition of replay-value so they can more precisely score it in reviews and engineer it during development. The problem with the old-school definition of replay-value is not only that it was subjective, it's nebulous as well. It's an emergent quality that is generated from the holistic nature of the game; unfortunately, such emergent qualities can be extremely difficult to engineer at the game development stage. It can be difficult to review old-school replay-value because it doesn't show up till some time much later after the initial play-through; this can be in conflict with current journalistic gaming publication cycles because the quality may not be easily discernible until long after an initial review is written and published (requiring a later amendment to the review or a re-review). Being able to quantify replay-value by the number of things to do or a strictly engineered number of replays through game necessary to attain completion would mitigate the problem in both cases. Unfortunately, for the gamer, the holistic experiential nature of the game may be lost in the process. The game reduces merely to completion of chores.
Video games are interactive. They can affect you and you can affect them. The technical game is just a series of tactical movements and decisions made in the course of the game to achieve an optimal or desired outcome. However, video games, because of their highly interactive nature, are able to go well beyond being technical games into being actual alternative experiences, and this, I feel, is where the real differentiation of old-school and new-school replay-value is visible. The old-school definition of replay-value is most likely attainable in those games which are explicitly design as self-consistent, coherent, holistic experiences that touch the gamer deeply and spiritually in a manner that, unfortunately, can not be easily predicted. The new-school definition of replay-value can be attained in just about any game that requires a certain level of repeat-play grinding in order to achieve particular outcomes, but this kind of gaming is not always experiential, nor is it always actually fun. To be fair, an experiential game is also not always fun, but because it has the greater potential to have a more profound effect on the gamer, at a spiritual level, it is more likely to be the kind of game that the gamer wants to play again simply to immerse himself again in that experience.
I believe this is why Final Fantasy VII is still such a revered game, even today. For many, myself included, it wasn't just a game; it was an experience (which is why I played the game, to completion, seven times; no doubt, others have played it more times to completion). Ico is another perfect example--a game that only achieved legendary status long after the game was no longer available and long after the rather foot-note-like reviews of it had been published; the game is extremely linear, but the experiential nature of the game is such to entice the play to play it multiple times purely for the enjoyment of playing it.
Yahtzee's signification of replay-value with the term "chocolate sauce" is probably a good description of what the old-school replay-value definition is really trying to convey. Replay-value is like eating a favorite food; you do it again to achieve nothing more than that blissful, pleasurable state of satisfaction you so enjoy that only comes from eating that particular food. Old-school replay-value is exactly like that. It's a flavor that just gives you a profound sense of pleasure and satisfaction, and you return to it only to achieve, again, the immersion into that state.
ADDENDUM: I also want to add World of Warcraft in its earlier incarnations, original vanilla up to about mid-Burning Crusade, as also being in the same class of experiential games that enticed repeat play for the pure pleasure of playing (this is why some many put so many hours into the game back in those days). Compare this to the later incarnations, especially during Firelands, where WoW became more just a collection of things-to-do.