Dicta are not part of the law of the case and thus are of NO FORCE AND EFFECT. If the dicta were that the day of the decision the sky was blue and cloudless, dicta are dicta and of no force and effect.
Which doesn't mean it doesn't exist.
The reality is, the only reason it's dicta is that Wong wasn't trying to be President. If he had in fact been suing to validate his eligibility for President then the exact same text you dismiss as dicta makes absolutely clear that he would be eligible. That logic doesn't go away because it's dicta. It doesn't stop existing because he wasn't trying to be President. That same reasoning will lead to the same answer when it's applied to a Presidential candidate.