"Delinquent" literally means "guilty of misdeeds," so a "delinquent gang" is a criminal gang, where the purpose of the gang is to commit crimes.
A similar phrase is a "gang of delinquents," which is a group of criminals. In theory, a "gang of delinquents" could just be a conincidental gathering of criminals and not a group dedicated to crime, but in practice the two phrases mean more or less the same thing.