This is more about level of preparation / past experience than age per se. The OP describes a “bright, self-motivated child in their late teens who is into maths” and is a few years ahead of their peers. The mentioned book might seem a bit easy or elementary for this particular kid. The two Berkeley Math Circle books might be better. https://mathcircle.berkeley.edu/books
You are right that a book aimed at well prepared Russian 12-year-olds in an extracurricular math circle might be fine for 16-year-old average American students.
You are right that a book aimed at well prepared Russian 12-year-olds in an extracurricular math circle might be fine for 16-year-old average American students.