I agree with you that 1600 calories per day is too low for a boy his age who is also active in boxing. I'm not exactly sure how many calories he'll be burning a day, but it's very possible that he could be burning between 500-1000 calories per day just in this new activity, at which point, if he's presently a bit soft and fluffy, his body will likely begin changing, and in a hurry.
Boxing is a great activity for a kid. I hope he enjoys it!