Technically, the Form 4457 is not about firearms, it is a "Certificate of Registration for Personal Effects Taken Abroad."
Its purpose is to document the fact that the goods you will be bringing back into the US with you when you return were not purchased abroad and, therefore, are not subject to various import taxes or import restrictions that may apply. Hence its application to any item of value (photo, computer, jewelry, etc.) that could be subject to an import tax when sold in the US.
The fact that the South Africa Police Services associate the Form 4457 to a "gun permit" is a loose interpretation. They apparently simply assume that if US Custom & Border Protection are willing to certify that you own the rifle(s) in the US, then it must be legal for you to do so.
Interestingly, this, in itself, is an erroneous assumption, because as amply stated by numerous folks above, CBP cannot physically verify that you are the owner, and does not verify that it is legal for you to own a rifle. They will just stamp the fact that individual XYZ showed up at their office with rifle of brand ABC serial #1234567.
I hope this helps