There are different types of debating, which may cloud the question; debating once or twice a year on a single prepared topic may be less informative for participants. Debating dozens of times a year on an active team is an entirely different experience. I would not be surprised at all if debate team participation has significant overlap with the rhetoric taught to students in ancient times.
Debating is an object lesson for the participants in how one can find (or should at least be able to find, if you're a good debater) arguments in favour of either side of any given issue.
Debating, especially impromptu debating, teaches quick thinking. It also teaches an ability to empathize with people on any side of an argument - you know, from experience after debating, that one can make good arguments in favour of an arbitrary side of a topic. You regularly work through points of view that you may not personally hold.
It's been said that math is learned at the end of a pencil - you learn it by working through it. Debating is the same - you learn empathy and understanding with points of view other than your own by working through them yourself.
Edit: all of this is from my experience in parliamentary debating eons ago. Things may have changed, if - as the article suggests - people can win without arguing the actual question they were given.