A guy with a big chip on his shoulder isn't going to do well. He's easy to play with, but even without manipulation he's going to wreck his life.
A lot of the Islamic world is like that, probably because the population is young, social structures are intensely patriarchal, employment opportunities suck, education is distorted by religious doctrine and the world is a very scary place. Just be glad the "The End of Men" isn't a video. Threats to patriarchal structures are not entirely imaginary.
But it's not just Islam. The anti-Japanese riots in China look awfully to Cairo; and does anyone remember burning cities in 1960s America?
So national rage isn't as simple as a cultural trait unique to Islam.
What about free speech, how simple is that?
As any high school student should be able to describe, we don't practice completely free speech in the US. The NYT mentions a couple of examples but Wikipedia has more ...
... the Miller test for obscenity, child pornography laws, speech that incites imminent lawless action, and regulation of commercial speech such as advertising. Within these limited areas, other limitations on free speech balance rights to free speech and other rights, such as rights for authors and inventors over their works and discoveries (copyright and patent), protection from imminent or potential violence against particular persons (restrictions on fighting words), or the use of untruths to harm others (slander)...
... Publishing, gathering or collecting national security information is not protected speech in the United States ... The unauthorized creation, publication, sale or transfer of photographs or sketches of vital defense installations or equipment as designated by the President is prohibited. The knowing and willful disclosure of certain classified information is prohibited ... It is prohibited for a person who learns of the identity of a covert agent through a "pattern of activities intended to identify and expose covert agents" to disclose the identity to any individual not authorized access to classified information, with reason to believe that such activities would impair U.S. foreign intelligence efforts..
Julian Assange could say something about national security and restrictions on free speech -- though the material he published was widely redistributed in the US without much consequence. The US didn't exercise blocks on web servers. Other information is more restricted. Although the wikipedia article on nuclear weapon design is pretty detailed, more practical 'make your own terror weapon' recipes are hard to find.
Even videos of this type of restricted material would be unlikely to provoke popular outrage. Neither would videos attacking religious beliefs, politicians, science (the GOP makes those) or history -- denial of American slavery, Amerindian genocide or the Holocaust are all protected speech.
The only exception I can think of would be child pornography. Videos that use children under the age of 12 in sexual or harmful activities are strictly illegal in the US and would create anger and disgust. I can't see riots, though and, of course, the Islamic reaction would be at least as negative.
National rage is not uniquely Islamic, but protected speech is pretty distinctly American. Perhaps a consequence of that protected speech is that while sticks and stones will trigger invasions, "names will never hurt us".