Without seeing the video you really have no idea on the conditions or the test itself.
First, the M16 and cleaning thing. Whether the M16 is used in the desert, Arctic, my basement, or Disney-world really doesn't change what's happening there: unless it's cleaned the powder residue from that direct impingement system is going to gum up the works eventually. It's an artefact of the design and the environment is really irrelevant as it's not foreign matter (sand) but matter from the system itself. So the M14 doesn't suffer from that but that's the result of having a piston versus skipping it.
Second, the M14 is going to be more sensitive to foreign matter introduced into the action as the action is open. Pour sand on an engine. No significant result. Pull the valve cover gaskets and repeat. Problems will result. The M16 having more of a "closed" action means it permits foreign matter to enter less than designs which have open actions.
Third, to the test itself. The test is accurate as far as it goes. Blow sand into the M14 and it's going to jam. Blow it at the M16 and it won't as the action is "sealed" to a certain extent.
Doesn't mean the test is logical or really that useful. If sand is blowing bad enough to enter the system that rapidly it won't be from a pile of it next to the gun being blown with compressed air. It'll be sand everywhere. Which means you'll not be able to see more than about 5 feet. So I guess the M14 wins that one as it's more sturdy and you're going to need that to beat people to death as they're going to be too close to shoot.
If sand is blowing that hard from a direction, turn the M14 so the floor plate is in the direction of the wind. There, sand isn't being blown into it. Holding the rifle sideways will decrease your use of the sight but, again, with visibility limited you're pretty much just shooting in a compass direction anyway.
If the sand is blowing that hard, and does regularly, do not lube the M14. With the chamber area being dry, and sand being dry, holding the rifle upside down will permit gravity to clean the sand out in a downward direction. Either pull the trigger in that orientation or turn it sideways. Again, visibility is causing more harm than sand getting into the weapon. Lube will permit the sand to stick.
So, yes, guns with open actions are going to jam with sand blowing around that that rate. "Action covers" existed for guns from the 1890s into the 1950s. Krags, M-1903s, SMLEs, and the M1 carbine. Probably others and later. It's to keep the action clean of debris in those situations. When the sand settles down visibility returns and you then ensure the gun isn't gummed up and start banging away. If somebody shows up before the sand dies down I'd suggest the use of an entrenching shovel. Sand doesn't jam those.
So the test is accurate as far as it goes. What it proves is M14s don't operate well in sand storms. Neither do humans. Nor motor transport. In other news, cars don't run well underwater, solar panels don't work well in thunderstorms, and pork doesn't sell well in Jordan.
Interested in reading more? I'd suggest tracking down a book titled: "a job of pipe." Royal Engineer in North Africa during the Rommel/Montgomery thing. During sand storms everyone pretty much tries to find a spot that it's not blowing up your nose or in your mouth. Masks help but aren't 100% effective. No doubt why the shooter in that film is wearing a gas mask. That'd get real old in the desert real fast.