Yes, the player has to want to pursue a graduate program of study at the new school, that is not offered at the current school.
In practice, it seems that for whatever reason, this is an easy technicality to get around.
I do not think that I have ever heard of a graduate transfer being denied by the NCAA.
http://www.ncaa.org/about/resources/...fer-division-i:
This so-called “graduate transfer” rule was intended to assist academically high-achieving students in pursuing a degree of interest that may not be offered at their undergraduate college. But it has become controversial in football and men’s basketball due to high-profile cases and as data have emerged showing that many transfers in those two sports earn few graduate credits and leave school when their athletics eligibility expires.