Chess, the king
Telling someone that an object is a particular chess piece - here, the king - conveys no useful information unless, for example, the person has learned the rules of chess but has never seen actual chess pieces. Then that knowledge becomes invaluable - you couldn't even place the piece in its starting position on the chessboard without it. Even beyond its various messages about language, this paragraph seems to address the holistic nature of knowledge emphasized by Sellars. Knowing one thing usually requires knowing a lot of other things. This theme threads through much of the discussion in these early Remarks.
In the second paragraph, a distinction is made between the situation of the first paragraph, in which it is assumed that the person to whom "This is the king" is directed knows the rules of chess, and the situation in which the person doesn't know the rules but can nonetheless play a game. The possibility of such an ability is explained as follows:
He might have learnt quite simple board-games first by watching ...
One possible interpretation of this is that one could have watched people playing "quite simple board games" - in particular, simple chess games using conventional pieces - and memorized the complete sequence of the moves constituting each individual game (at least in principle - W says one could "imagine" someone's doing so). Having been told that a new object is called "king" - ie, that it plays the role of the conventional piece that the player knows by that name - the player then knows that in each memorized game the moves made by the conventional king should instead be made using the new object. Ie, in memorizing whole chess games, identifying the new piece with the king "informs [the player] of the use of the piece  because ... the place for it was already prepared".
Whether this interpretation of W's analogy is right or wrong, it resonates with me because it is consistent with my suspicion that verbal inputs are understood, and responses to them are formulated, in chunks larger than individual words. Ie, analogous to memorizing whole chess games (in essence, learning for each game a response to every move by an opponent), we perhaps learn context-dependent responses to "verbal moves" by conversational partners. And in that sense, the place in a language game for a new word or phrase to be used in individual games (verbal exchanges) has been prepared if the word or phrase can replace a word or phrase in those previously learned verbal exchanges.