This is a simple assertion, without any reasoning or support provided. Maybe it is correct, and maybe it isn't, but the issue is sufficiently dispute by reasonable people to require more than "this is the way it is".
Personally, I think it's wrong. Legal, permanent residents who are not themselves U.S. citizens still have political allegiance to their country of citizenship, and so even their children would be excluded.
It is absurd to believe that the Fourteenth Amendment confers the boon of American citizenship on the children of illegal aliens.
It isn't "absurd". It may be wrong (for reasons other than the "subject to the jurisdiction thereof" logic given above), but it is not such a simple, clear legal issue that disagreement is "absurd".
It seems to me he starts with feudalism and common law to arrive at an understanding of jurisdiction, but I would never use a word like “absurd” unless all alternative reasoning was obviously in error.