Even if some definition were found to be adequate, we do not have any fixed boundaries in mind, even implicitly, when we use the word "game." It is perhaps possible to establish some sort of artificial boundary for what we call "game," but this boundary would neither prescribe nor describe how we actually use the word "game."
Wittgenstein is fighting against the notion of fixity of meaning. This notion sees words as having a fixed meaning regardless of their context. We know what a word means not because there is some fixed meaning attached to it with which we are familiar, but because we know how to use that word in certain contexts. In section 80, Wittgenstein takes the example of a chair that periodically vanishes and then reappears. We would not be sure whether to call this a chair or a strange illusion. Our word "chair" only has a definite meaning in the contexts that we are familiar with. In a less magical vein, we can also imagine a flat, angled plank of wood that has a small notch for resting. We can sit on this object and rest our back against it, but do we call it a chair? Not necessarily. The word "chair" might seem to have fixed meaning because there are a number of objects that we unhesitatingly would call chairs, but there are also borderline cases where we may or may not want to call an object a chair. To a large extent, whether or not we call an object a chair depends on the context.
Wittgenstein was the first thinker to recognize the great philosophical importance of rules, and uses them cleverly in relation to fixity of meaning. There are two primary ways in which the boundaries we might apply to definitions of words are like rules in a game. First, the rules of a game do not cover all cases. The rules of hockey say that a player gets a two-minute penalty for hooking. But what if a player pulls out a gun and shoots his opponent? There is nothing in the rules to cover this eventuality, largely because it has never happened before and is not likely to happen. This example is like the case of the vanishing chair in section 80. Rules and boundaries are only clear when dealing with the situations we are familiar with, but no set of rules or boundaries can cover all possible situations.
Second, rules in themselves do not remove all doubt. In section 86, Wittgenstein talks about a table as a rule, where we can correspond items in the left-hand column with items in the right-hand column. But how do we know to read left to right? Do we need a rule to tell us to do that and not to read in some sort of criss-cross pattern? And if this rule is expressed in terms of arrows pointing from one column to the other, do we need a further rule to tell us how to read the arrows? Wittgenstein's point is not that rules are useless, but that there is a point where we simply follow a rule without any explicit justification.