Nice of you to exclude the last part of that law which reads: “was intended to exclude from its operation children of ministers, consuls, and citizens or subjects of foreign States born within the United States.”
CARLISLE V. UNITED STATES CASE(1872):
“Every foreigner born residing in a country owes to that country allegiance and obedience to its laws so long as he remains in it, as a duty upon him by the mere fact of his residence and that temporary protection which he enjoys, and is as much bound to obey its laws as native subjects or citizens. This is the universal understanding in all civilized states, and nowhere a more established doctrine than in this country.
Independently of a residence with intention to continue such residence; independently of any domiciliation; independently of the taking of any oath of allegiance or of renouncing any former allegiance, it is well known that by the public law, an alien or a stranger born, for so long a time as he continues within the dominions of a foreign government, owes obedience to the laws of that government and may be punished for treason or other crimes as a native-born subject might be unless his case is varied by some treaty stipulation.”
Every foreigner born residing in a country owes to that country allegiance and obedience to its laws so long as he remains in it...an alien or a stranger born, for so long a time as he continues within the dominions of a foreign government, owes obedience to the laws of that government and may be punished for treason or other crimes as a native-born subject might be unless his case is varied by some treaty stipulation.
Thus a foreign national here is subject to the jurisdiction of the United States, up to and including treason! Unless you are exempted by treaty, you are under the full jurisdiction of the United States when you are on US soil. And that includes treason.
Why include treason if you weren't subject to the jurisdiction of the US? How can I - a US citizen - commit treason within Germany, without being a German citizen? Treason itself is the act against your Government; here's the definition from Merriam Webster's dictionary:
1 : the betrayal of a trust : treachery
2 : the offense of attempting by overt acts to overthrow the government of the state to which the offender owes allegiance or to kill or personally injure the sovereign or the sovereign's family
Clearly the second definition is of import here, and we see it as an act to overthrow the state to which the offender owes allegiance! How can a foreign national owe allegiance to the US unless they are inherently subject to our full jurisdiction (being here voluntarily means accepting such jurisdiction and hence, granting at least limited allegiance). The case of Carlisle v US makes that explicitly clear:
Every foreigner residing in a country owes to that country allegiance and obedience to its laws so long as he remains in it.
Meaning that - if your father is a British or Canadian or Venezuelan citizen - while present in the US (unless here as an ambassador, or other exempted individual) - he owes allegiance and obedience to the US. The jurisdiction of the US is supreme over that foreign national.
If anything, your quote strengthens the case further that President Obama was subject to the full jurisdiction of the US at birth, and his father was likewise subject to that jurisdiction.