No, it doesn't. It merely says in this one set of circumstances there is no doubt. The judge goes on to recognize other possible birth circumstances without attempting to resolve the "doubt" because it is irrelevant to the case.
Sorry, but there's no reason to talk about other definitions if they aren't relevant. And even after this section on the definition, they continue to talk about other circumstances and maintain a distinction between the children of natives and the children of aliens. For example, later in Minor v. Happersett, it says, "From this it is apparent that from the commencement of the legislation upon this subject alien women and alien minors could be made citizens by naturalization, and we think it will not be contended that this would have been done if it had not been supposed that native women and native minors were already citizens by birth." Keep in mind, according to the definition they used, native = born in the country to parents who are citizens.