Just to be sure, it looks like a serial number since it makes sense that it would be, record keeping wise. A serial number on such records is a standard and common process. And it is at roughly at least 90% probable from inference of the coincidence of the number with the given birth date and births for HI that year, yet this is a guess and not direct knowledge of the process in Hawaii at the time.
Are you saying that this is a birth order serial number based upon direct or documented knowledge of the official Hawaiian process at the time, in August 1961?