It doesn't matter where/with whom he lives unless he qualifies as YOUR dependent child; don't get confused between the part about his having a dependent child (and those definitions/qualifications) and being one. You have to be able to claim him as a dependent for him to have been a dependent child and I don't think you can do that so he was not, himself, a dependent child.

He just has to:

be age 25 but under 65 at the end of the year,
live in the United States for more than half the year, and
not qualify as a dependent of another person.