IME, facebook games are generally set up so that the easiest course of action is to send an invitation to everyone on your friends list, and often people who do not play the game will be included in lists for requesting in-game help from friends. For the games I play, I often have to manually sort through the list to select only the people who I know already play that game. Or, if the game itself has a list of only game-players, there is usually an incentive to request from the general friends list instead (thus sending requests to people who don't play that game).
I think it's highly unlikely that your friend is intending to send you an individual, personal request to join the game, especially after six requests without a personal message. It's most likely that they're just clicking through whenever the game asks them to send requests to their friends list. It's certainly not rude to ignore the requests or block the game entirely.