"Language Game" as a Philosophical Term
Wittgenstein's "language game" concept was on many levels designed to "push back" against the overwhelming impression a dictionary makes on our concept of "meaning". We get to mentally roll back to that earlier time in childhood development when we lived surrounded by meaning but without the benefit of a dictionary.
Apparently we learn to appreciate meaning well before we become cognizant that words have definitions. The "language game" concept is calculated to rekindle that understanding.
But is the concept of "language game" itself well-defined? Here is where you need to be a great writer like Wittgenstein to deliberately allow the notion of "fuzzy borders" into one's philosophy.