Quoits

The idea that quoits—a game in which players toss rings at a stake, hoping to encircle it—originated with the "Greek or Roman discus" does not seem to me to hold up. The discus was flung for distance; quoits is a game of accuracy. The fact that each is circular is not sufficient to link the two historically.

Those who subscribe to the Greco-Roman origin use it as a basis for quoits coming to Britain during the Roman occupation. The game of quoits ("coiting") in England during the reign of Edward III, and again during the reign of his successor, Richard II, was outlawed in favor of pastimes such as archery, which would translate to readiness in battle. This was duplicated in the Statutes of Kilkenny (see here and here) by Edward's son, Lionel of Antwerp, in his rôle as viceroy of Ireland.

(Ironically, quoits was referred to as "manly and healthy amusements" in 1836 in a Washington, DC, advertisement for the available amusements at a nearby coffee house.)

The similarity between quoits and the game of horseshoes suggests that the game might have started with people idling their time by throwing spare horseshoes at a stake or peg. That assumes, however, that "horse shoes" in the past were the ring- or U-shaped pieces of metal they are now.

And that is something worth looking into in more detail.