That video is more than a little off the mark. Almost every western jet airliner has a powerful trim system. They need it for a variety of reasons, and in the 737 max, the MCAS system utilises this trim system to accomplish its task. The important thing is that the trim system itself can malfunction regardless of the presence of MCAS; they can run away. That's effectively what happened to both of these airplanes.
A trim runaway is a rare event, and there are several layers of protection guarding against them. First, they are wired so that multiple failures need to occur before there is a failure. Next, there is a semi-automatic brake that will jam it solid in the event that it does runaway. The brake is activated by the pilot pushing or pulling the stick in the direction opposite of the trim. He'd do that as naturally as the driver of a car might press on the brake if the car began to accelerate uncommanded. This second feature, the brake, is bypassed in the 737MAX if the MCAS is triggered. It has to be as the system is assuming that the pilot might be the cause of the problem. So if the MCAS fails, it's going to cause a runaway trim.
HEre's the thing - none of this matters. There are two switches in all Boeing jet airliners that will instantly disable the trim system. And there is a manual wheel right next to that that enables manual control of the trim. If the trim acts up in any way, the drill is to immediately kill the trim with those two switches and trim manually. Neither one of those crews did that in good time. The Ethiopian crew did eventually switch the switches off. If memory serves, it was the very green FO that did so, in fact, but then someone switched them back on again.
In short, a trim runaway is apt to happen in any jet airliner, and in any Boeing especially, the drill is exactly the same - you disable the power trim and trim manually. You don't hesitate, you simply do it, for obvious reasons.
In short, both crews failed to fly the airplane. The fault lies with Boeing, their respective airlines, and a culture that relies too heavily on automatics on the flight deck and dilutes the practice of good airmanship. This is especially true in third world countries, where traditions are relatively young and the depth of experience across an airline is small, but it's also true of a lot of low cost airlines with a relatively young pilot body.