Italian here, Roman actually.

The Roman salute has not origin in ancient history.

It was formalized by Gabriele D’Annunzio, a sick fascist poet and writer, as a salute for his proto-fascist troops with which he occupied Fiume in modern-day Croatia, having been inspired this painting.

So yea, the roman salute is a fascist salute, invented by a fascist, for a fascist occurrence and to call it roman is a disservice to Rome and history in general.