English public schools and universities played an important role in the codification of football in the mid-nineteenth century.

At around the same time, Oxford University slang attached the suffix -er to many shortened nouns, leading to the popular names of both soccer and rugger. World Soccer, the English football magazine, was founded in 1960.

So it's very likely that several of the players in the football match would have known the game as soccer. Whether John McCutcheon was aware of this, I cannot say.