Hi S.,
You have some great and interesting responses, but I wanted to provide feedback from a nutrition undergrad perspective.
Binge eating is usually classified as consuming 2,000 - 5,000+ calories in one sitting. So even if he eats a whole loaf of bread, 4-6 yogurts, and real fruit, I don't think it's enough to be medically classified as binge eating. Another criteria for this classification is time, which you didn't mention in your post but, this behavior has to take place for at least 3 months to be considered medically relevant. If it's been less than that, then kudos to you for being proactive!
One thing you'll want to monitor for is weight gain. It's one thing if he eats 2,000 calories in one sitting but doesn't gain any weight yet it's another thing if he eats all this food and begins to gain weight. The weight gain is a sign that the eating is not from hunger, but due to other issues. The issues can and often range greatly from comfort eating, to low self-esteem, to anxiety, to physical medical ailements. I see other suggestions as to why people may binge eat have already been suggested by other group members, and are entirely plausable. Most athletes will gain weight in the off-season as well, so keep that in mind when your monitoring for weight gain. It's normal for athletes to gain as much as 10 - 15 lbs in the off-season, depending on height, and isn't a sign of disordered eating.
Recognize that the one and only area you have control in this situation is the food choices he has in the house to binge on. He is much less likely to "binge" if he is consuming a nutritionally balanced, healthy diet. Keep unhealthy food to a minimum for him to have access to, even if this means a little healthier eating for the rest of the family for a while. Let me stress bare minimum, because this is the only thing you can control.
I would definitely talk to him and see if he knows why he does this, if you haven't done so already. My guess is that he told you something that doesn't appear to make sense or he told you he doesn't know why, and that's why your posting here. Unless this behavior has gone on for quite a while (with no end in sight) or he is experiencing excessive weight gain, I would hold off on making it a huge deal. You don't want your attention to somehow re-inforce the behavior.
The last thing I would suggest is trying to find ways to help HIM avoid this become a habit. At his age, you still have the power of influence, so I would use it! It's possible that what he is doing is perfectly normal for the changes taking place in his body right now, while simultaneously creating a lifelong (or maybe even a long-term) habit of eating huge amounts of food at night even after his body has slowed it growth. If you decide to talk to him about it, mention the risk of long-term habits developing and that he needs to try and not engage in this behavior because it could cause bad habits for him in the future. It's really hard to stop a night-binging route, once it's good and established, and I read of another person who posted that their son had an issue with this. Emphasize how much better it is (routine-wise) to eat throughout the day. It might be a difficult concept for a 13-year old to grasp, but he'll probably remember it for in the future.
Good luck! Feel free to message me if you want additional help!
K.