Does Nigeria *legally* define black or Nigerian every time they select their leader? It's just not that good a question tbh.
Discussion
No, but they have some legal system for deciding who becomes a President. An election, with eligibility criteria, etc. Same with Japan, or Europe, or any other advanced nation. And those nations don't have "racial" requirements.
Birthright citizenship, having one's family be in the USA for X number of years... etc. Those are possible criteria.