Wikipedia says:
Naturalization in Japan requires the applicant to renounce their current citizenship(s) after the naturalization takes place. The Japanese government does not have strict rules for the naturalization process, even though the documents that need to be collected for application from applicant's home country might take quite some time. Basic naturalization requirements differ from person to person regardless what country the applicant is from and depending on applicant's current status in Japan. Unlike most other countries, the applicant does not have to be a permanent resident to be eligible to apply for Japanese naturalization.[3]
The criteria for naturalization are provided in Article 5 of the Nationality Act:[4]
- Continuous residence in Japan for five years or more
- At least 21 years old and otherwise legally competent
- History of good behavior generally, and no past history of seditious behavior
- Sufficient capital or skills, either personally or within family, to support oneself
- Stateless or willing to renounce foreign citizenship
Note number 5 and the last paragraph: I would say that Fitzgerald will not be eligible as he would have renounced his NZ citizenship.
This is a set of Japanese nationality rules. I'm almost certain this has no bearing on FIFA. He was born here and has not played for another country and is therefore eligible. Its the other way around where it might become a problem. They are only allowed 4 foreign players in j-league teams. If his fifa nationality is NZ, despite official Japanese nationality, he may well count as a foreign player and not be considered good enough for a visa spot.