I'm not sure but I guess it's an expression of "feeling" or Vedanā -- e.g. the feeling that, "This is pleasant" versus "This is not pleasant".
I say that because the book starts with discussing whether you should maintain your motorcycle, based on whether your doing so leads to your having a good time when you're riding (I think there's a passage with an analogy about riding on a sunny day on a well-tuned machine versus riding in the rain on a machine that's breaking down). The word "feeling" shows up frequently in the first chapter,
Another memorable passage, near the climax, is when he explains the Greek idea of arete -- I think that the example which he gives, i.e. "And
may they say, as he returns from war, ‘He is far better than his father.’" appears to be an example of pride or conceit.
I'm not sure whether all that is what Buddhists would call "the direct experience of the moment". I couldn't tell you about Zen but the practice of "guarding the sense door" might (I'm not sure) involve being aware of what you sense (e.g. aware of contact: contact between light plus eye plus consciousness-of-seeing, and so on for all six senses), without becoming over-involved in how you may feel about that, in the feelings which you develop as a consequence of that sensory contact.
On the other hand part of what I think is good about the book is when he decides that the question "What is good?" is a more important or fundamental question than "What is true?" (i.e. when he contrasts the Sophists with Aristotle). I think the question of "What is good?" (i.e. Quality) corresponds not only to "feelings" but also "virtue" (right behaviour, righteousness, morality) ... and not only "virtue" but also the question of whether things are "beneficial" or "skillful" instead of harmful. And I think that corresponds to Buddhist concepts -- one of which is sila, which isn't just elemental but fundamental to Buddhism-as-it's-taught -- and another is the Buddhist term "ariya", which is translated "noble" or right, and is used when naming, "the noble truths", "the noble eight-fold path", "the noble sangha".