Some scholars try to date the gospels very late. Try to imagine yourself writing about Jesus as He talked about "not one stone left on another." Could you resist the temptation to add "and so it is to this day?" Me neither.
Ecclesiastes never mentions games. (We laughed at the idea of what the Preacher would say about basketball. I know people who've watched Star Wars a dozen times, but who watches basketball re-runs?) By the same rule, that makes it pre-Hellenist. "Runners race to reach the end, and they end where they began; this also is vanity." No way he'd have omitted it.