My stock made from leftover rotisserie chicken is very gelatinous. I thought only uncooked chicken bones made stock gelatinous. Any explanation?
Fat will thicken a stock, but will not make it gelatinous. Gelling comes from collagen which comes from the bones or — in my opinion — even better from the joints.

My experience is that this is easier to achieve from a cooked bird than a raw one rather than the other way around.  The gelling may have locked up some of the fats, but you also may not have had as much as you expected even with the added skin just because rotisserie chicken tends to have some cooked out or rendered.

My anecdotal experience is that the longer you simmer with bones and cartilage, the more collagen is released and cooking down concentrates it more giving more gelling to the stock. I tend to call mine consomme, but that is really only correct if it has been clarified.

If you really want a rich, well gelled one, get some chicken feet and include it in your stock pot!  For the opposite, if you want no gelling, my practice is to increase the amount of meat, limit the bones and cartilage and do not simmer long, and I myself would normally do that with raw poultry rather than cooked, simmering for minutes, not hours.