Games help with creativity. Seeing something you enjoy, such as X part of Y game, and wanting to create something similar, either video or some other aspect of design. What it doesn't teach is proper social skills unless it's an MMO of some sort and they actively become engaged in the social aspect.
I think its fairly obvious that games are a fun way to learn. The old fashioned way that schools teach is going to become out dated really quick in my opinion. For example when I was in school and lets say in math class the teacher would set you 30 algebra questions to do in x amount of time, you had kids like me that would finish in 5 or so minutes and spend ages waiting to know if I answered correctly or not while other kids would take 20 minutes and maybe only have answered half. Games provide that instant gratification when you beat a challenge. I'm assuming that teacher that used DS's to teach used Brain Training as he mentioned all the games were typical shelf bought, which provides instant an instant reward when you answer correctly.
Tablets are very nice for education purposes. In a few decades, when they get cheap enough, they will replace the textbooks. It will be pretty easy to have a tablet with lessons and exercises which may resemble games.
I agree that games can help kids with creativity, they can also learn a lot while playing. The network is plenty of educational portals with games for children - they can learn a foreign language, learn a little about nature, develop interests. Recently I found a cool site about Antarctica and krill with cool games for kids - Krill Facts. Must try