I think you misread that, in context it circles back to the American one. For more context see here under origins. The American version was very much in the timeline with the inspiration: https://en.m.wikipedia.org/wiki/Nazi_salute

Also worth reading: https://web.archive.org/web/20240719151050/https://www.workingclassicists.com/post/the-antiquity-to-alt-right-pipeline

The Nazi’s love of America and Rome plus the whole America being based on a lot of Roman stuff (Look at your money motifs… Columns on Lincoln Memorial, White House, etc.), is a whole… thing. People forget the Rome idolization too, but it goes hand in hand with the American stuff.

https://press.princeton.edu/books/hardcover/9780691172422/hitlers-american-model