Thank you for pointing this out.
TLDR - You are right, notarisation is NOT required.
The reason I assumed it was required is the document is called an affidavit. In many jurisdictions across the world (and some in the US), by definition, an affidavit is required to be notarised. I just looked it up, and apparently the requirements is trending to be removed over the last several years (but is still required in many places). So it basically depends on the prevailing law of the jurisdiction in which you are submitting the affidavit is required to be notarised or not.
For the purposed of the i751, the submission is to a federal body and I understand Federal law does NOT require affidavits to be notarised so long as it is sworn with the following wording:
"(1)If executed without the United States: “I declare (or certify, verify, or state) under penalty of perjury under the laws of the United States of America that the foregoing is true and correct. Executed on (date).
(Signature)”.
(2)If executed within the United States, its territories, possessions, or commonwealths: “I declare (or certify, verify, or state) under penalty of perjury that the foregoing is true and correct. Executed on (date).
(Signature)”.