Given that the short film was produced in Turin (according to the Italian Wikipedia), it is likely that that the Aeroclub of Turin (1908) has more information on this aircraft.
On their website they describe the history of aviation in Turin in the 1909-1915 period(in Italian). Around that time, Turin was a center of aviation in Italy (and it still is).
There were several aircraft manufacturers, including the automobile factory FIAT (Fabbrica Italiana Automobili Torino) which at some point produced Farman aircraft under license.
One of their first employees (employee no.3) was Alessandro Cagno. He was, among other roles, the company's racing team driver. In 1909 he lost interest in car racing and turned to aviation. He became the 10th pilot in Italy, on a Farman aircraft. There are several pictures of him in his Farman III on the internet, which looks very much like the aircraft in the short film.
Below is a picture from 1911 of Cagno in his Farman III in Venice.
By Unknown - over 100 years old. Source: wikipedia
Especially this picture looks very similar to what can be seen in the film, including hills in the background.
More video material of the Farman III can be found here:
You can see that there were several variations on the model.
It may be Cagno's aircraft in the film, or another Farman. Looking at the list of early aviators in Italy, the majority of them got their license in either a Farman or a Bleriot. The latter aircraft looks very different.
Source: Contact! The Story of the Early Aviators, Henry Serrano Villard ISBN: 0-486-42327-1