For a pre-teen a laptop might be better, although the hardware is less powerful than a desktop of the same price. I don't talk about the fitness for OBS, I'm just talking about the child handling the computer. He will probably want to take it with him, even if only at home. A desktop is stationary. In the past, I recommended friends that have children in that age desktops, but all of them told me that this isn't suited to children. Children want devices they can carry around. My friends bought laptops for their children (aged 12+ or 13+) and I never heard a complaint. And as far as I observed it, the children used the laptops, they didn't collect dust, and they didn't destroy it.
On the other hand, a $300 laptop isn't suited for use with OBS. Not at all. You have to invest more for this use case.
But children will use computers these days. If you buy a more expensive laptop, it will not be in vain, since it will have other uses for it. Simple games like minecraft are (or were, I'm not up to date with current children's demands) very popular, for example.