That doesn't mean it's available to someone simply because of their age, Jim - the sprit of the eligibility criteria (especially, but not only, the "Is my institution eligible?" section) is clear enough. If eligibility was only about being of a certain age, it wouldn't be called an student discount; and questions like whether a student's institution was eligible, would be irrelevant.
"Student and teacher discounts are available to individual teachers, students, and staff members".
Not "to individual teachers and any 13 year old or older kid".
Being able also to use the software for non-educational purposes is obviously just a practical, common sense "easement" to the conditions of the educational licence - probably because such a restriction would be unenforceable.