It is a short-form birth certificate. "Certification of Live Birth" is a fancy name for "short-form birth certificate". You are attempting to create an artificial distinction by ever referring to a "short-form birth certificate" as a birth certificate, and pretending that only a "long-form birth certificate" can be called a birth certificate. You are failing. There are no situation in which the state of Hawaii would issue one of these to someone not born in the state of Hawaii.
Wrong. The short-form birth certificate issued by the state of Hawaii has all of the elements required by the state department for issuance of a passport:
http://www.factcheck.org/elections-2008/born_in_the_usa.html
"The certificate has all the elements the State Department requires for proving citizenship to obtain a U.S. passport: "your full name, the full name of your parent(s), date and place of birth, sex, date the birth record was filed, and the seal or other certification of the official custodian of such records." The names, date and place of birth, and filing date are all evident on the scanned version, and you can see the seal above."