I think you're confusing separate issues. The idea of having contests where two mathematicians would each issue challenge problems to the other was primarily an event in the Middle Ages. This idea then continued in some forms with people like Fermat (later Middle Ages or early Renaissance depending on how you define things) who would issue challenges to others to prove what they had already proven. What Orthonormal is doing actually more closely resembles a practice from the 19th century where when multiple people were racing to solve a problem first, they'd every so often deposit a sealed envelope with some reputable independent body to verify issues of priority.