Your grandfather naturalized as a U.S. citizen with his father. Naturalization as a U.S. citizen renounces any other citizenship.
My grandfather was born in the United States and was always a citizen. He didn't naturalize, never had a green card, and was 23 years old when his father naturalized. Oh, by the way, that was a few months after my grandfather's brother was killed in Normandy. I guess to you he wasn't a citizen either when he died for this country.
Naturalization Oath
Maybe you can point to the part of your link that says your adult children are also naturalized by this oath.