The reason the quality can't be named isn't because it's vague or general : Alexander suggests it's highly precise. The problem is that language is too vague and indeterminate to grasp the quality. He illustrates this by showing how several words catch aspects of the quality but insufficiently : alive, whole, comfortable, free, exact, egoless, eternal.
The other thing that strikes me as interesting on re-reading this chapter is how explicitly Alexander ties it together with some notions of normativity and function. He points out that the quality has the flavour of being true to self, or lacking inner-contradictions; and that this isn't a relevant thing to talk about in the context of physics and chemistry entities. Atoms just are without being able to say whether they're true to themselves or lacking in inner-contradictions. It's only living things like people (and buildings and towns and "complex systems") which have the possibility of having the quality.
In this sense, it's grasping at the idea of normativity; of there being a space within which the system's way of being can be "right" or "wrong".
He also gives examples of systems which lack "wholeness'" due to being unstable. (A gully whose sides are being washed away by rain.) And this point, it sounds like he thinks that being under-destruction is a symptom of lacking the quality. (Although of course entropy must be attacking everything, however much of the quality is has. )
Does this make his notion of the quality akin to some kind of Milikanian, adaptionist account or normativity? Function is that which contributes to survival or maintaining or reproduction of the thing that has it. Maybe it's getting close to AutoPoiesis?
Maybe some connection with my discussion of TheScientificStatusOfALife
What has the quality?
Though I say it myself, I'm pretty confident that Gbloink! (up to 1.5) had it, despite the bugs and weaknesses. And I'm equally certain that the new Gbloink! (1.8) has lost the quality, despite having more stuff, trying to solve the most serious problems with 1.5, and the program itself having been refactored into much, much better shape. This is one of the reasons I've been listlessly sitting on it for a couple of years!!! (Could be related to what AlexSchroeder calls FeatureKarma. Or good old fashioned software "bloat". Though I think the problem is deeper. It's lost the fabulous result to effort ratio of the original. All the new stuff adds complexity to the user's experience, but the music isn't much different or better. (Maybe see also GrognardCapture)
Wiki, of course, has the quality. But maybe you can't say that about a piece of software, maybe only a piece of software and a community. So some wikis due to their code and what people do with it.
"The tao that can be named is not the Tao." By defining it, we lose it. Thus, do not define.