If you are wondering what to get for a boy that is turning 13 and you just decide to go to a toy store that you went to, last year, and pick up something out of the shelf and gift him that, then I am truly sorry for you and the boy. Things are getting a little more complex as they enter this interesting psychosocial stage of development. It is not just psychosocial but a lot of it is also paired up with the biological; the hormonal changes.
A lot of times, how you treat a teenager is dictated by what society sets as the norm. Clues for this can be taken from the media that they are exposed to; both for you to learn how to treat them and for you to understand why they are the way they are. Speaking of media, I would say, at this age, television is one of the biggest influence. All the teenage movies really tell kids how to behave and what to expect from others. It’s not that your kids are weak too learn from it, but is jut rather a fact.
Peers would be one of the greatest influence as well. If the peers of a boy who is about turn 13 are already 13 and have received some sophisticated board games or so, then it would not be a great idea to get that boy a one-piece toy. Again, media will come in. All of this and other things about their peers can be learned from social media and not just school. I will not go in detail in gender roles in this small article, as that is a separate debate. But if you just want to be on the safe side, try getting something for a 13-year-old boy from LTG online blogpost.