I know for the Naval Academy, you don't get the salary. Even if you were previous enlisted you are no longer paid your salary, though I believe the 4 years in the academy count towards retirement.
It is a stipend, and stipends are allowed by the NCAA. The handbook in your link calls it a stipend. Since there is a hard cap on how much cash you can actually take from your "pay", I would call it a stipend.
1 - https://www.usna.edu/Admissions/Student-Life/General-Informa...