you could say exactly the same thing to support the opposite interpretation. "if you wanted to refer to multiple words you could just say that (i.e "Player u for a sequence of words u)
i agree that if the possible domain of what u could refer to was specified, then that should take effect. since it isn't we need to decide upon a sensible default; i think the default should be whichever behaviour is likely to be used most often, and i think it will be more often desirable to match a single word than multiple words.