If the Principal of a school says that unruly boys will not be allowed to play games and if someone concludes that it is perfectly fine for unruly girls to play games, what is the fallacy called as?
This would be described by a "correct" usage of the exception that proves the rule. By specifying boys when perhaps you don't need to (you could say "unruly children"), the contrary of your statement applies for those children who are not boys.
Quite often "the exception that proves the rule" is taken to mean "X therefore not X in general", which is logically incorrect, but not what is meant here.
Generally the utterance "boys can't play" does in fact imply "girls can". Because if both could play, or none could play, you either wouldn't say anything or would say "children". There is more information in what you say.
It's less clear in cases where there is an adjective, as it is difficult to determine the assumptions that are implicitly made. If you say "boys can't play" it's clear this is applied with a group of children in mind. But if you say "unruly boys can't play" its unclear whether the group you have in mind: all the children, the unruly ones, the girls, or less likely the not-unruly girls and the unruly boys.
So the "unruly" case is using the exception that proves the rule where perhaps it shouldn't. Is it a fallacy with a name, who knows. The exception-that-proves-the-rule-when-it-doesn't-fallacy?
I'm not sure it has an official name, although it's close to denying the antecedent. The essence of the exchange is that one person says "if (unruly boy) then (no play)" and is taken to imply "if (unruly not boy) then (play)".
Here the denial is not actually of the antecedent. The more exact structure would be something like $(A\land B) \rightarrow C$ therefore $(A\land\negB)\rightarrow \neg C$.