It's a meaningless distinction to say that it distinguishes between two classes of children but not two classes of citizen. The Constitution itself distinguishes between two classes of citizen. One, NBC, is a requirement for presidential office. The other, citizen of the United States (and a lesser class), is a requirement for Congress. That the court recognizes TWO ways citizens can be created, doesn't mean there is only one class of citizenship per way. One can be a citizen at birth via the naturalization statute, such as in the naturalization act of 1790.
So they just got finished saying that there are only two classes of citizens: born citizens and naturalized citizens.
It doesn't say "class" in this section, while it does talk about "class" in reference to NBC and those citizens recognized by "some authorities" who were born in the country without regard to their parents. The latter class of citizenship (of which there is doubt) lumps together both children born of citizens, and those NOT born of citizens. IOW, it's not two separate classes of children, but TWO separate classes of citizen: One is NBC and the other are born citizens whose citizenship would be in doubt.
I really don't see how you can read it that way. (I'm not even sure what "born citizens whose citizenship would be in doubt" means.) But I've been reading birther legal analysis for a couple of years now, and it usually leaves me thinking "how can anyone read it that way?" so there's probably no point in pursuing it further right now.
FIFY.