You can’t fault the name for accuracy. It was a game, said to combine skill and chance, that really did consist of chucking farthings, that is, throwing small coins. The farthing was a British coin, one quarter of a penny (it comes from an Old English word for a fourth part), which went out of use in 1960, even before decimalisation of the currency in 1971.
The Sports and Pastimes of the People of England by Joseph Strutt, dated 1838, has a detailed description, albeit with a different coin:
I have seen a game thus denominated played with halfpence, every one of the competitors having a like number, either two or four, and a hole being made in the ground with a mark at a given distance for the players to stand, they pitch their halfpence singly in succession towards the hole, and he whose halfpenny lies the nearest to it has the privilege of coming first to a second mark much nearer than the former, and all the halfpence are given to him; these he pitches in a mass towards the hole, and as many of them as remain therein are his due; if any fall short or jump out of it, the second player, that is, he whose halfpenny in pitching lay nearest to the first goer’s, takes them and performs in like manner; he is followed by the others so long as any of the halfpence remain.
It seems, though, that coins weren’t always used, sometimes being replaced by rough-cast leaden counters, called dumps because they were dumpy in shape.
Like so many games, this one was disliked by serious-minded folks, in part no doubt because of the implied warning in John Arbuthnot’s History of John Bull (1755): “He lost his money at chuck-farthing, shuffle-cap, and all-fours.” The last of these was a card game, while in shuffle-cap money was shaken up in a hat, at least according to the Oxford English Dictionary, to what effect I’ve been unable to discover.