The Great Depression caused Hitler's rise to power. Economic troubles and people looking for someone to blame. Such is the way with Fascism. Nationalism in the guise of patriotism, excluding large parts of society as "not one of us", dismantling civil liberties in the guise of security, politics in bed with the wealthy and powerful.....sound familiar?
I guess you didn't watch the add. He stated facts and said nothing about it being the cause in any way shape or form. It's a dishonest reporting tool, in which the author injects what's not there and give his biased opinion of what subject thinks, when he has no bases for it!
The point of the message what the authoritarian Nazi and Ottoman Empire governments had an easier time of committing their genocides because they enacted complete gun control.
I know this foresure. To quote the late great Heston, "You can take my guns from my cold dead hands!"