In theory, yes. If the job the person is doing would otherwise be performed by a US citizen (inc. yourself), then the person requires a work permit. Whether or not remuneration is received is not always relevant.

There are a number of instances of alien grandparents being refused entry to the US when they comment that they plan to babysit their grandchildren, since that is technically taking away employment from US citizen babysitters.

In practise, a 16-year old is highly unlikely to be questioned about illegal work when he says he is visiting the USA for 6 weeks, staying with a friend of his dad and college scouting.