He didn't use the example of 'game' but ...

I'm reading a 19th-century author, Richard Whately, who was the Anglican Archbishop of Dublin. He wrote the first modern (not entirely Aristotelian) logic textbook in the English-speaking world (Elements of Logic [1826] -- which influenced C. S. Peirce). He also wrote an influential textbook on rhetoric (Elements of Rhetoric [1828]). Both works were standard textbooks in the UK and US for many decades.

In Elements of Rhetoric, Whately disabuses the reader of

the common error of supposing that a general term has some real object, properly corresponding to it, independent of our conceptions; — that, consequently, some one definition in every case is to be found which will comprehend every thing that is rightly designated by that term; — and that all others must be erroneous: whereas, in fact, it will often happen, as in the present instance, that both the wider, and the more restricted sense of a term, will be alike sanctioned by use, (the only competent authority,) and that the consequence will be a corresponding variation in the definitions employed; none of which perhaps may be fairly chargeable with error, though none can be framed that will apply to every acceptation of the term. (Richard Whately, Elements of Rhetoric [1828], p. 2)