I don't think they downplayed the seriousness one little bit.
Depends on the size of the comet of course, but anything a mile or more in diameter would extinguish civilization and most (over 99 percent) of humanity. The EMP would take care of most or all of the comm networks worldwide.
The only shelter would be underground, and it would have to involve prepper type stockpiling of supplies, as the surface temperature would rise unbearably, then drop unbearably.
They do point out increased precipitation (that would assume impact on water, which is 7:3 vs a land impact) but much of that would be freezing rain, snow, and ice, leaving a circular "ice age" glacial area on part of the Earth. After the cloud cover blocked all sunlight, a condition that would last for months or years, the falling temps would cause a halt to the hydrologic cycle, meaning, no rain anywhere. The early rise in atmospheric temps might melt off all high-altitude snow and ice, and until the remaining fresh waters in streams and rivers froze as the temps crashed, everything else would low out into the salty oceans.