What quality do top schools look for, besides normal requirements?
Graduate admissions is very different from undergraduate admissions. A lot of what you may read online about undergraduate admissions does not apply to graduate admissions.

(Traditional) applicants to undergraduate programs are understood to be (generally) young. They haven't had much of a chance to prove themselves yet through meaningful accomplishments. So in undergraduate admissions, it is not uncommon to look for intangible "qualities" that speak to a candidate's ability to be successful in areas that they haven't yet had a chance to prove themselves in. That's just because many highly qualified prospective undergraduate students don't have many tangible achievements (simply due to lack of life experience, not lack of potential.)

In contrast, applicants to graduate programs have more experience, whether academic, life, or professional experience. Prospective graduate students are simply not nearly as "unknown" as prospective undergraduate students. They have had more of a chance to collect some meaningful accomplishments. Thus in graduate admissions, tangible achievements weigh far more heavily. 

So while motivation, curiosity, etc. may be useful qualities for a graduate student, admissions committees are interested in what you have done (which may show that you have these qualities). They're not interested in having you tell them what qualities you believe you have.

Sometimes if a candidate lacks academic achievements but has meaningful achievements in other areas (e.g. entrepreneurial), these can help. (That may be what was implied by "you probably have something else in you that's extremely unusual".)