I let my 13 year old nephew play videogames in the arcade while I had a quiet dinner. He had his KTTW card with charging priveleges so he could get something to eat at the resort while playing games. He also had a cell phone and strict instructions as to where he could and couldn't go.
Someone can correct me if I'm wrong, but I think 13 year olds are allowed to be 'unsupervised' at DisneyQuest. Lots of teens hang out there.