This was BVG - before video games. Mostly. :)
I'm not quite sure but it sounds like a Rollerball ripoff but I dont recall hearing of any such movie. I also think most italian/Europe post apocalyptic movies of 1970's would not include "American Football" in its theme.
But I really think it might be a Lampoon films of the 1970's like American Raspberry (which I'd seen under the title called Prime Time), Amazon Women on the Moon (but its from the 1980's) or the others (sorry I have not seen them but I'll list them for you) The Groove Tube, Tunnel Vision, The Kentucky Fried Movie.
or even something from SNL/SCTV...
It does sound like a Lampoon trailer...
Wish you luck in finding it... :)
PS... I dont recall seeing this in American Raspberry, but there is a scene where two men gather their hunting gear, walked up a tower and started to shoot at the students....