This video calls into question the wisdom of using the infamously rapid fire 8mm GPMG, the MG42. In fact, it questions nearly all automatic firearms in German usage. Certainly, modern machine guns avoid such a heavy calibre and high rate of fire -so was this video on to something?
Doctrinal differences aside, the video largely seems to ignore a lot of the selling points of the German weaponry and upsell the accuracy of American weapons (something dubious at best when you get into actual combat) while ignoring their faults.
One thing to note first - you mention "heavy caliber" when referring to the 8mm cartridge. While larger in bore than the ~7.62mm 30-06 cartridge that was the American standard for the war, 8mm Mauser is roughly analagous to any other "full sized" rifle cartridge of the time. Wartime loadings for the two were almost identical in terms of muzzle energy, and in their original (military) and postwar (commercial) incarnations, .30-06 actually had significantly more energy.
The biggest selling points of the German GPMGs of the war - the MG-34 and MG-42 - were their flexibility. Unlike most other nations, the Germans had combined all of their machinegun roles into a single platform. Every other belligerent had specific light, heavy, and vehicle machineguns, while the MG-34 (and later MG-42) would combine these roles into a single common gun. From that respect, they performed spectacularly well. They were about as mobile as traditional LMGs like the Bren, ZB-26, Type 99, or BAR, and they had special tripod mounts that allowed them to operate like a heavy machinegun for sustained, accurate long-range fire. While not particularly unusual by most country's standards, the MG-34 and MG-42 also had quick-change barrels, with the MG-34's barrel being notable for being exceptionally easy to change without really having to get out of cover or change the position of the gun.
American machineguns, particularly the ones shown in the video, had plenty of issues. The 1919A6 was the "light" machinegun used by Americans in the demonstrations in that video, and it came into service as a stopgap thanks to the shortcomings of the BAR as a light machinegun. Unfortunately, the 1919 wasn't as versatile as the German machineguns. It was a full 6 pounds heavier than the MG-34 despite changes like a lighter barrel made to reduce weight, and while the barrel was more feasible to replace than on earlier 1919 models (which required the gun to be completely field-stripped), replacing the barrel on the 1919A6 required the crew to pull the barrel out of the front of the barrel shroud. The water-cooled machinegun shown was viable in its specific role (sustained fire from a static position), but it lacked the flexibility of air-cooled guns, let alone the German GPMGs. You'll notice that even in the video when they're explaining the Machinegun platoons they show air-cooled 1919s - those tended to be the more common weapon than the water-cooled 1917.