The Form FS-240 is not a birth certificate, such as is issued by a government-authorized bureau or office of vital statistics, because consular officers are not authorized to assume a foreign local or state vital statistics function.
Except that his says Rota, Spain, not Okinawa, Japan, etc.
It kind of looks to me like the form FS-240 is meant to dilute the definition of a US citizen, in that it is only a report, not a certification. I do not know what kids born abroad after 2010 are supposed to use for birth certificates.