This comparison isn't actually in Dubious Shards, I think. Ken Hite would pick better wording.
Anyway, it's basically correct, just as long as you remember that there is no value judgement on the terms- D&D can be quite "adult" in one sense. It's just that the core themes of the game is one closely related to childhood. D&D characters develop; there's a fairly linear "growing up" phase, and as they do so they face ever increasing challenges. If that's not a metaphor for childhood, I dunno what is. D&D's target "get 'em hooked" age was 11-12, or thereabouts, after all.
Many (though not all) World of Darkness games focused on a sudden transformation setting a person apart from their contemporaries, a transformation that carried with it newfound power, responsibility and frightening consequences. If that's not a metaphor for becoming a teenager, I dunno what is. That was their target audience, after all.
The metaphor breaks down when you get to Call of Cthulhu, which isn't a metaphor for adulthood.
Just divorce yourself from the terms as insults and just look at the central metaphors- most WoD games (especially the oWoD, and Exalted) can be viewed as metaphors for adolescence using horror tropes like vampires. D&D's core ethos is one of gradually increasing responsibility and capability- you go from the 1rst level baby to the 20th level adult, and so on.
Also remember, they're just metaphors, they don't really mean anything for gaming...